BECs Surface "Electron Density"

The video below is showing Bose Einstein Condensate system (BECs) surface. A High Temperature Superconductor or substrates formed on the top of the system to close it; and these substrates are unique materials made of copper and oxygen called cuprates and combine with Titanium, Dysprosium, and Silicon. The light is reflected in an angle of (45) degrees which is spread in very tiny bits due to electron density.

I would like to make a short explanation to expose the whole experiment from the beginning (from day one). The idea is about the discovery of Higgs boson which is incarnated within the Rugosa corals. To create Bose Einstein Condensate system (BECs) (6) Rugosa corals are needed that means that the total (6) represents Higgs boson.

Higgs boson is a monopole that means that (2) parts (Rugosa corals) will work as south poles, another (2) will work as north poles and the two left will be the neutrals or mediators between the south poles and the north poles.

By adding seawater a magnetic field is created, at this stage the most important path is that the system should be isolated or closed and this happens by the ejection of the carbon atoms first, this is why we saw that Graphene and diamond where first to appear on the surface as first layers to be generated. After that the copper and the oxygen form compounds with light metals such as Titanium, Dysprosium and Silicon; they travel to the surface to form (3) compounds (TiCuO, DyCuO and SiCuO). The atoms within the system loose their electrons and become equal in mass; the electrons rush to the surface to make it very dense and participate in the reflection of light.

I do believe that the compounds (TiCuO, DyCuO and SiCuO) are the perfect materials to be used as superconductors in room temperature to innovate the 3D chip and transistor manufacturing as they have a very high electron density.

The pictures below are showing Bose Einstein Condensate system (BECs) surface during my experiment on Higgs Boson inside the system.

Unconditional Substrates are the Key to Innovation

This post comes with complementary information to the two earlier posts of “True Bose Einstein Condensed System Phase( 3)”.

Definitions:

1-In quantum mechanics, the uncertainty principle: is any of a variety of mathematical inequalities asserting a fundamental lower bound on the precision with which certain pairs of physical properties of a particle, such as position (x) and momentum p, can be simultaneously known. The more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. The original heuristic argument that such a limit should exist was given by Werner Heisenberg in 1927.

Mathematically, the uncertainty relation between position and momentum arises because the expressions of the wave function in the two corresponding bases are Fourier transforms of one another (i.e., position and momentum are conjugate variables). A similar tradeoff between the variances of Fourier conjugates arises wherever Fourier analysis is needed, for example in sound waves. A pure tone is a sharp spike at a single frequency. Its Fourier transform gives the shape of the sound wave in the time domain, which is a completely delocalized sine wave. In quantum mechanics, the two key points are that the position of the particle takes the form of a matter wave, and momentum is its Fourier conjugate, assured by the de Broglie relation.

2- The Fourier transform, named for Joseph Fourier, is a mathematical transform with many applications in physics and engineering. Very commonly, it expresses a mathematical function of time as a function of frequency, known as its frequency spectrum. The Fourier integral theorem details this relationship. For instance, the transform of a musical chord made up of pure notes (without overtones) expressed as amplitude as a function of time, is a mathematical representation of the amplitudes and phases of the individual notes that make it up. The function of time is often called the time domain representation, and the frequency spectrum the frequency domain representation. The inverse Fourier transform expresses a frequency domain function in the time domain. Each value of the function is usually expressed as a complex number (called complex amplitude) that can be interpreted as a magnitude and a phase component. The term "Fourier transform" refers to both the transform operation and to the complex-valued function it produces.

3- In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat propagation.

4- Harmonic analysis: is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms. In the past two centuries, it has become a vast subject with applications in areas as diverse as signal processing, quantum mechanics, and neuroscience.

5- In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform.

6- Time frequency transform: In signal processing terms, a function (of time) is a representation of a signal with perfect time resolution, but no frequency information, while the Fourier transform has perfect frequency resolution, but no time information. As alternatives to the Fourier transform, in time–frequency analysis, one uses time–frequency transforms to represent signals in a form that has some time information and some frequency information – by the uncertainty principal, there is a trade-off between these. These can be generalizations of the Fourier transform, such as the short-time Fourier transform, the Gabor transform or fractional Fourier transform, or can use different functions to represent signals, as in wavelet transforms and chirplet transforms, with the wavelet analog of the (continuous) Fourier transform being the continuous wavelet transform.

7- The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (t) is:

where:

A, the amplitude, is the peak deviation of the function from its center position.

ω, the angular frequency, specifies how many oscillations occur in a unit time interval, in radian per second

φ, the phase, specifies where in its cycle the oscillation begins at (t = 0).

When the phase is non-zero, the entire waveform appears to be shifted in time by the amount φ/ω seconds. A negative value represents a delay, and a positive value represents an advance.

7-1 This wave pattern occurs often in nature, including ocean waves, sound waves, and light waves.

A cosine wave is said to be "sinusoidal", because it is also a sine wave with a phase-shift of (π/2). Because of this "head stars", it is often said that the cosine function leads the sine function or the sine lags the cosine.

7-2 In two or three spatial dimensions, the same equation describes a travelling plane wave if position (x) and wave number (k) are interpreted as vectors, and their product as a dot product. For more complex waves such as the height of a water wave in a pond after a stone has been dropped in, more complex equations are needed.

7-3 In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number obtained by multiplying corresponding entries and then summing those products. The name "dot product" is derived from the centered dot "  " that is often used to designate this operation; the alternative name "scalar product" emphasizes the scalar (rather than vector) nature of the result.

When two Euclidean vectors are expressed in terms of coordinate vectors on an orthonormal basis, the inner product of the former is equal to the dot product of the latter. For more general vector space, while both the inner and the dot product can be defined in different contexts (for instance with complex numbers as scalars) their definitions in these contexts may not coincide.

In three dimensional space, the dot product contrasts with the cross product, which produces a vector as result. The dot product is directly related to the cosine of the angle between two vectors in Euclidean space of any number of dimensions.

8- Signal processing: is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, or measurements of time-varying or spatially-varying physical quantities. Signals of interest can include sound, images, and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals, and many others.

9- The goals of signal processing can roughly be divided into the following categories.

9-1 Signal acquisition and reconstruction, which involves measuring a physical signal, storing it, and possibly later rebuilding the original signal or an approximation thereof. For digital systems, this typically includes sampling and quantization.

9-1-1 Data acquisition: is the process of sampling signals that measure real world physical conditions and converting the resulting samples into digital numeric values that can be manipulated by a computer. Data acquisition systems (abbreviated with the acronym DAS or DAQ) typically convert analog waveforms into digital values for processing. The components of data acquisition systems include:

a) Sensors that convert physical parameters to electrical signals.

b) Signal conditioning circuitry to convert sensor signals into a form that can be converted to digital values.

c) Analog-to-digital converters, which convert conditioned sensor signals to digital values.

9-2 Quality improvement, such as noise reduction, image enhancement, and echo cancellation.

9-3 Signal compression, including audio compression, image compression, and video compression.

9-4 Feature extraction, such as image understanding and speech recognition.

9- 5 In communication systems, signal processing may occur at OSI layer (1), the Physical Layer (modulation, equalisation, multiplexing, etc.) in the seven layer OSI model, as well as at OSI layer (6), the Presentation Layer (source coding, including analog-to-digital conversion and data compression).

10- The Open Systems Interconnection (OSI) model: is a product of the Open Systems Interconnection effort at the International Organization for Standardization. It is a prescription of characterising and standardising the functions of communication system in terms of abstraction layers. Similar communication functions are grouped into logical layers. A layer serves the layer above it and is served by the layer below it.

According to recommendation X.200, there are seven layers, labelled (1) to (7), with layer (1) at the bottom. Each layer is generically known as an (N) layer. An "N+1 entity" (at layer N+1) requests services from an "N entity" (at layer N).

10-1 The (OSI) seven layers:

OSI Model
Polymer.doc	Data unit	Layer	Function
Host layers	Data	7. Application	Network process to application
		6. Presentation	Data representation, encryption and decryption, convert machine dependent data to machine independent data
		5. Session	Interhost communication, managing sessions between applications
	Segments	4. Transport	End-to-end connections, reliability and flow control
Media layers	Packet/Datagram	3. Network	Path determination and logical addressing
	Frame	2. Data link	Physical addressing
	Bit	1. Physical	Media, signal and binary transmission

11- Line vector: A line vector is a vector, such as a force, that is constrained to lie along a given line.

12- A transistor: is a semiconductor device used to amplify and switch electronic signals and electrical power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current flowing through another pair of terminals. Because the controlled (output) power can be higher than the controlling (input) power, a transistor can amplify a signal. Today, some transistors are packaged individually, but many more are found embedded in integrate circuit.

13-1 Semiconductor devices: are electronic components that exploit the electronic properties of semiconductor materials, principally silicon, germanium, and gallium arsenide, as well as organic semiconductor. Semiconductor devices have replaced thermionic devices (vacuum tubes) in most applications. They use electronic conduction in the solid state as opposed to the gaseous or thermionic emission in a high vacuum.

13-2 An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice. It is different from the positron, which is an actual particle of antimatter, whereas the hole is just a fiction, used for modelling convenience.

The electron hole was introduced into calculations for the following two situations:

If an electron is excited into a higher state it leaves a hole in its old state. This meaning is used in Auger electron spectroscopy (and other x-ray techniques), in computational chemistry, and to explain the low electron-electron scattering-rate in crystals (metals, semiconductors).

In crystals, band structure calculations lead to an effective mass for the charge carriers, which can be negative. Inspired by the Hall Effect, Newton's law is used to attach the negative sign onto the charge.

13-3 In quantum mechanics, and in particular quantum chemistry, the electronic density is a measure of the probability of an electron occupying an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typically denoted as either ρ(r) or n(r). The density is determined, through definition; by the normalized N-electron wave function which itself depends upon (4N) variables (3N spatial and N spin coordinates). Conversely, the density determines the wave function modulo a phase factor, providing the formal foundation of density functional theory.

13-4 An integrated circuit: or monolithic integrated circuit (also referred to as IC, chip, or microchip) is an electronic circuit manufactured by lithography, or the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material. Additional materials are deposited and patterned to form interconnections between semiconductor devices.

13-5 Electrical mobility: is the ability of charged particles (such as electrons or protons) to move through a medium in response to an electric field that is pulling them. The separation of ions according to their mobility in gas phase is called Ion mobility spectrometry, in liquid phase it is called electrophoresis.

13-6 Semiconductor materials: are nominally small band gap insulators. The defining property of a semiconductor material is that it can be doped with impurities that alter its electronic properties in a controllable way.

Because of their application in devices like transistors (and therefore computers) and lasers, the search for new semiconductor materials and the improvement of existing materials is an important field of study in materials science.

Most commonly used semiconductor materials are crystalline inorganic solids. These materials are classified according to the periodic table groups of their constituent atoms.

14- An organic semiconductor is an organic material with semiconductor properties. Single molecules, short chain (oligomers) and organic polimers can be semiconductive. Semiconducting small molecules (aromatic hydrocarbins) include the polycyclic aromatic compounds pentacene, anthracene, and rubrene. Polymeric organic semiconductors include poly(3-hexylthiophene), poly(p-phenylene vinylene), as well as polyacetylene and its derivatives. There are two major overlapping classes of organic semiconductors. These are organic charge-transfer complexes and various linear-backbone conductive polymers derived from polyacetylene. Linear backbone organic semiconductors include polyacetylene itself and its derivatives polypyrrole, and polyaniline. At least locally, charge-transfer complexes often exhibit similar conduction mechanisms to inorganic semiconductors.

15- A charge-transfer complex (CT complex) or electron-donor-acceptor complex is an association of two or more molecules, or of different parts of one very large molecule, in which a fraction of electronic charge is transferred between the molecular entities. The resulting electrostatic attraction provides a stabilizing force for the molecular complex. The source molecule from which the charge is transferred is called the electron donor and the receiving species is called the electron acceptor.

The nature of the attraction in a charge-transfer complex is not a stable chemical bond, and is thus much weaker than covalent forces. The attraction is created by an electronic transition into an excited electronic state, and is best characterized as a weak electron resonance. The excitation energy of this resonance occurs very frequently in the visible region of the electro-magnetic spectrum, which produces the usually intense color characteristic for these complexes. These optical absorption bands are often referred as charge-transfer bands (CT bands). Optical spectroscopy is a powerful technique to characterize charge-transfer bands.

Conclusion from definitions:

The line vector function is the shortest function with respect to time. The uncertainty principle missed to use this function to deal with time frequency, in contradiction the principle was based on Fourier transform which makes the time frequency more complicated and less fast, means a loss of time during the process. The consequences are to limit the development of applications in many domains of technologies such as instruments of measurement used in quantum mechanics, and in the computer based applications.

I already introduced three materials (TiCuO, DyCuO, and SiCuO), these materials are compounds of copper and oxygen called cuprates, they are a new family of high temperature superconductor, and can resolve the problem of room temperature superconductor and also they could be the solution to resolve the problem cited above. Once a chip and a transistor are built using these materials; efficiency in time frequency will be corrected at 100%. This is a huge gain of time by achieving C in E =MC2. The problem of the observer of particles and wave like particles will be resolved; means it will be possible to see a particle as a particle and as a wave in the same time. Also most of the persisting problems within the OSI model will be resolved by adding an 8^th layer which is chips and transistors based on (TiCuO, DyCuO and SiCuO).

The suggested materials are organic metals designed in molecule shape, and they are superconductors formed illegally to the human known physics laws. 

TiCuO, DyCuO and SiCuO reflecting light on BECs surface due the high electron density.

TiCuO, DyCuO and SiCuO reflecting light on BECs surface due the high electron density.

TiCuO, DyCuO and SiCuO reflecting light on BECs surface due the high electron density.

Note: Definitions are from Wikipedia

Statistical Indifference

Hypothesis

In this post I would like to introduce you to my hypothesis about matter and wavelike particle duality. The principle of the observation of any phenomena as a wave or a particle in quantum mechanics could be done in a different efficient manner.

The quantum mechanics is based on uncertainty and probability principles (operators); let’s say that these principles are not needed any more because the observer has found a perfect tool to measure particles and their waves in their ground state in the same time; once this is achieved then all operators of correspondence will be exhausted.

The answer to how to build a new understanding of quantum mechanics is hidden in the creation of a true Bose Einstein Condensate system (BECs) where Higgs boson (Rugosa corals) is a fundamental element. Particles and their waves are at their inertial state; means their mass, energy and velocity is at a very low unit but not zero and acceleration equals zero. (BECs) is a perfect system where to develop quantum mechanics theories, as natural conditions are created to the observer to make an adequate measurement to the particles and their waves in the same time.

The most serious problem of quantum mechanics is called “wave function collapse” which is not resolved yet, because of the inability to observe this phenomenon directly, and the tools used for this observation destroy the information needed to understand this phenomenon.

The latest innovative technologies are using many kind of materials to develop the superconducting quantum interference device (SQUID) which is used by researchers in quantum mechanics for experiments. So the solution to quantum mechanics is hidden within the superconductor material used to build the right tools needed.

What we already know from the last post that true Bose Einstein system (BECs) is able to produce a special material which is a high temperature superconductor based on copper oxide, such compounds are the perfect solution to fabricate highly developed tools to make an accurate measurement without uncertainty.

The production of HTS compounds TiCuO, DyCuO and SiCuO which have a crystalline structure of copper oxide superconductors with multi layer planes is a perfect solution to innovate the innovative technologies of the semiconductor industries.

By this occasion I would like to offer samples of (TiCuO, DyCuO, and SiCuO) to companies engaged in the fabrication and design of semiconductor devices to analyze these magnificent superconductor materials.

Photograph showing TiCuO, DyCuO and SiCuO on the surface of  BEC system

Definitions

1- De Broglie “Wave-like- Matter and wave-particle duality”:

"The fundamental idea of [my 1924 thesis] was the following: The fact that, following Einstein's introduction of photons in light waves, one knew that light contains particles which are concentrations of energy incorporated into the wave, suggests that all particles, like the electron, must be transported by a wave into which it is incorporated... My essential idea was to extend to all particles the coexistence of waves and particles discovered by Einstein in 1905 in the case of light and photons." "With every particle of matter with mass m and velocity v a real wave must be 'associated'", related to the momentum by the equation:

where λ  is the wavelength, h is the plank constant, p is the momentum, m is the rest mass, v is the velocity and c is the speed of light in a vacuum."

This theory sets the basis of wave mechanics. It was supported by Einstein, confirmed by the electron diffraction experiments of Davisson and Germer, and generalized by the work of Schrödinger

2- Niels Bohr Complementarity: is a fundamental principle of quantum mechanics, closely associated with the Copenhagen interpretation . It holds that objects governed by quantum mechanics, when measured, give results that depend inherently upon the type of measuring device used, and must necessarily be described in classical mechanical terms. Further, a full description of a particular type of phenomenon can only be achieved through measurements made in each of the various possible bases — which are thus complementary. The principle was developed and introduced by Niels Bohr in 1927.

Bohr model of atom

3- Werner Heinsenberg  uncertainty principle: is any of a variety of mathematical inequalities asserting a fundamental lower bound on the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known. The more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. The original heuristic argument that such a limit should exist was given by Werner Heinsenberg in 1927. A more formal inequality relating the standard deviation of position σx and the standard deviation of momentum σp was derived by Kennard later that year (and independently by Weyl in 1928).

4- Schrödinger's cat: is a thought experiment, sometimes described as a paradox, devised by Austrian physicist Erwin  Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be alive or dead, depending on an earlier random event. Although the original "experiment" was imaginary, similar principles have been researched and used in practical applications. The thought experiment is also often featured in theoretical discussions of the interpretation quantum mechanics. In the course of developing this experiment, Schrödinger coined the term Verschränkung (entanglement).

5- The double-slit experiment: sometimes called Young's experiment, is a demonstration that matter and energy can display characteristics of both waves and particles, and demonstrates the fundamentally probabilistic nature of quantum mechanical phenomena. In the basic version of the experiment, a coherent light source such as a laser beam illuminates a thin plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate. The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen, a result that would not be expected if light consisted strictly of particles. However, on the screen, the light is always found to be absorbed as though it were composed of discrete particles or photons. This establishes the principle known as wave-particle duality. Additionally, the detection of individual photons is observed to be inherently probabilistic, which is inexplicable using classical mechanics.

6- The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho). Mathematically, density is defined as mass divided by volume. 

7- Intencity (heat transfer)

Spectral intencity. Specific (radiative) intencity. Radiative transfere. The Eddington approximation. The Eddington approximation is a special case of the two stream approximation. It can be used to obtain the spectral radiance in a "plane-parallel" medium (one in which properties only vary in the perpendicular direction) with isotropic frequency-independent scattering. It assumes that the intensity is a linear function.

8-In physics, interference is a phenomenon in which two waves superimpose to form a resultant wave of greater or lower amplitude. Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, and surface water waves. It is actually a phenomena in which a light wave from two or more openings spaces strikes an opposite surface, the pattern observed is in form of dark and light patches due to the high or low amplitude of light respectively.

8- 1 Mechanism

The principle of superposition waves: states that when two or more waves are incident on the same point, the total displacement at that point is equal to the vector sum of the displacements of the individual waves. If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the magnitude of the displacement is the sum of the individual magnitudes – this is constructive interference. If a crest of one wave meets a trough of another wave then the magnitude of the displacements is equal to the difference in the individual magnitudes – this is known as destructive interference.

Constructive interference occurs when the phase difference between the waves is a multiple of 2π, whereas destructive interference occurs when the difference is π, 3π, 5π, etc. If the difference between the phases is intermediate between these two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values.

9- In organic chemistry, a carbonyl group is a functional group composed of a carbon atom double-bounded to an oxygen atom: C=O. It is common to several classes of organic compounds, as part of many larger functional groups.

The term carbonyl can also refer to carbon monoxide as a ligand in an inorganic or organometallic complex (a metal carbonyl , e.g. nickel carbonyl).

10- Diploid (indicated by 2n = 2x) cells have two homologous copies of each chromosome, usually one from the mother and one from the father. Nearly all mammals are diploid organisms (the tetraploid viscacha rats Pipanacoctomys aureus and Tympanoctomys barrerae are the only known exceptions as of 2004), although all individuals have some small fraction of cells that display polyploidy. Human diploid cells have 46 chromosomes and human haploid gametes (egg and sperm) have 23 chromosomes.

Retroviruses that contain two copies of their RNA genome in each viral particle are also said to be diploid. Examples include human foamy virus, human T-lymphotropic virus, and HIV.

11- Polyploidy: is the state where all cells have multiple sets of chromosomes beyond the basic set. For example, in triploids 2n = 3x, and in tetraploids 2n = 4x. The chromosome sets may be from the same species or from closely related species. In the latter case, these are known as allopolyploids (or amphidiploids, which are allopolyploids that behave as if they were normal diploids). Allopolyploids are formed from the hybridization of two separate species. In plants, this probably most often occurs from the pairing of meiotically unreduced gametes, and not by diploid–diploid hybridization followed by chromosome doubling.

12- The magnetic moment induced by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect and modern measurements on paramagnetic materials are often conducted with a SQUID magnetometer.

The magnetic moment: of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it. A loop of electric current, a bar magnet, an electron, a molecule, and a planet all have magnetic moments.

13- The magnetic Dipole: both the magnetic moment and magnetic field may be considered to be vectors having a magnitude and direction. The direction of the magnetic moment points from the south to north pole of a magnet. The magnetic field produced by a magnet is proportional to its magnetic moment as well. More precisely, the term magnetic moment normally refers to a system's magnetic dipole moment, which produces the first term in the multi-pole expansion of a general magnetic field. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object.

14- Chemical shift: A spinning charge generates a magnetic field that results in a magnetic moment proportional to the spin. In the presence of an external magnetic field, two spin states exist (for a spin 1/2 nucleus): one spin up and one spin down, where one aligns with the magnetic field and the other opposes it. The difference in energy (ΔE) between the two spin states increases as the strength of the field increases, but this difference is usually very small, leading to the requirement for strong NMR magnets (1-20 T for modern NMR instruments). Irradiation of the sample with energy corresponding to the exact spin state separation of a specific set of nuclei will cause excitation of those set of nuclei in the lower energy state to the higher energy state.

For spin 1/2 nuclei, the energy difference between the two spin states at a given magnetic field strength are proportional to their magnetic moments. However, even if all protons have the same magnetic moments, they do not give resonant signals at the same field/frequency values. This is because this dependent on the electrons surrounding the proton in covalent compounds. Upon application of an external magnetic field, these electrons move in response to the field and generate local magnetic fields that oppose the much stronger applied field. This local field thus "shields" the proton from the applied magnetic field, which must therefore be increased in order to achieve resonance (absorption of rf energy). Such increments are very small, usually in parts per million (ppm). The difference between 2.3487T and 2.3488T is therefore about 42ppm. However a frequency scale is commonly used to designate the NMR signals, even though the spectrometer may operate by sweeping the magnetic field, and thus the 42 ppm is 4200 Hz for a 100 MHz reference frequency (rf).

15- SQUIDs are being used as detectors to perform magnetic resonance imaging (MRI). While high field MRI uses precession fields of one to several teslas, SQUID-detected MRI uses measurement fields that lie in the microtesla regime. Since the MRI signal drops off as the square of the magnetic field, a SQUID is used as the detector because of its extreme sensitivity. The SQUID, coupled to a second-order gradiometer and input circuit, along with the application of gradients, are the fundamental entities which allow a research group to retrieve noninvasive images. SQUID-detected MRI has advantages over high field MRI systems, such as the low cost required to build such a system, and its compactness. The principle has been demonstrated by imaging human extremities, and its future application may include tumor screening.

15-1 Device fabrication

The device is typically fabricated by first depositing a thin film of a superconducting metal such as aluminium on an insulating substrate such as silicon. Probably the most common commercial use of SQUIDs is in magnetic property measurement systems (MPMS). These are turn-key systems, made by several manufacturers, that measure the magnetic properties of a material sample. This is typically done over a temperature range from that of 4 K to roughly 190 K, though higher temperatures mean less precision.

16- The superconducting tunnel junction: (STJ); also known as a superconductor–insulator–superconductor tunnel junction (SIS); is an electronic device consisting of two superconductor separated by a very thin layer of insulating material. Current passes through the junction via the process of quantum tunnelling. The STJ is a type of Josephson junction, though not all the properties of the STJ are described by the Josephson effect.

17- Quantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the sun, and has important applications to modern devices such as the tunnel diode. The effect was predicted in the early 20th century and it's acceptance, as a general physical phenomenon, came mid-century.

Note: Definitions are from Wikipedia