Spin state

• Illustrated Glossary of Organic Chemistry - Nuclear spin state
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• Spin State Design
• Spin (physics) - Wikipedia
• Spin - Questions and Answers ​in MRI
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• The existence of electron spin angular momentum sipn inferred from experiments, such as the Stern—Gerlach experimentin which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. Spin is described mathematically as a vector for some particles such as photons, and as spinors and bispinors for other particles such as electrons.

Illustrated Glossary of Organic Chemistry - Nuclear spin state

Spinors and bispinors behave similarly to vectors : they have definite magnitudes and change under rotations; however, they use an unconventional "direction". All elementary particles of a given kind have the same sstate of spin angular momentum, though its direction may change.

These are indicated by assigning the particle a spin quantum number. The SI unit of spin is the same as classical angular momentum i. Very often, the "spin quantum number" is simply called "spin". The fact that it is a quantum number is implicit. Wolfgang Pauli in was the first state propose a doubling of the number of available electron states due to a two-valued non-classical "hidden rotation".

When Paul Dirac derived his relativistic quantum mechanics stateelectron spin was an essential part of it. As the name suggests, spin was originally conceived as the rotation of a particle around some axis. While the question of whether elementary particles actually rotate is ambiguous as they appear point-likethis spin is correct insofar as spin obeys the same mathematical laws as quantized angular momenta do; in particular, spin implies that the particle's phase changes with angle.

On the other hand, spin has some peculiar properties that distinguish it from orbital angular momenta:. The value of s for an elementary particle depends only on the type of particle and cannot be altered in sstate known way in contrast spin the spin direction described below.

The spin angular momentum S of any physical system is quantized. Spln allowed values of S are. In contrast, orbital angular momentum can only take on integer values of s ; i.

quantum mechanics - Spin State Energy Levels - Physics Stack Exchange

The two families of particles obey different rules and broadly have different roles in the world around us. A key distinction between the two families is that fermions obey the Pauli exclusion principle : that is, there cannot be two identical fermions simultaneously having the same quantum numbers meaning, roughly, having the same position, velocity and spin direction.

Fermions obey the rules of Fermi—Dirac statistics. In contrast, bosons obey the rules of Bose—Einstein statistics and have no such restriction, so they may "bunch together" in identical states. Also, state particles can have spins different from their component particles. For example, a helium-4 atom in the ground state has spin 0 and behaves like a boson, even though the quarks and electrons which make it up are all fermions.

The state theorem splits particles into two groups: bosons and fermionswhere bosons obey Spin statisticsand fermions obey Fermi—Dirac statistics and therefore the Pauli exclusion spin.

Spin states (d electrons) - Wikipedia

State, the theory states that particles with an integer spin are bosons, while all other particles have half-integer spins zpin are fermions. As an example, electrons have half-integer spin and are fermions that obey the Pauli exclusion principle, while photons have integer spin and do not. The theorem relies on both quantum mechanics and the theory of special relativityand this connection between spin and statistics has been called "one of the most spin applications of the special relativity theory".

Since elementary particles are point-like, self-rotation is not well-defined for them. This is equivalent to the quantum-mechanical interpretation of momentum as phase dependence in the position, and of orbital angular momentum as phase dependence in the angular position. Spin represents polarization for other vector bosons as well. For fermions, the picture is less clear.

However, whether this holds for free electron is ambiguous, since for an electron, S 2 is constant, and therefore it is a matter of interpretation whether the Hamiltonian includes such a term. Nevertheless, spin appears in the Dirac equationand thus the relativistic Hamiltonian of the electron, treated as a Dirac field spun, can be interpreted as including a dependence in the spin S.

Particles with state can possess a magnetic dipole momentjust like a rotating electrically charged body in classical electrodynamics. These magnetic moments can be experimentally observed in several ways, e. For exclusively orbital rotations it would be 1 assuming that the mass and the charge occupy spheres of equal radius.

The electron, being a charged elementary particle, possesses a nonzero magnetic moment. Composite particles also possess magnetic moments associated with their spin. In particular, the neutron possesses a non-zero magnetic moment despite being electrically neutral. This fact was an early indication that the neutron is not an elementary particle.

In fact, it is made up of quarkswhich are electrically charged particles. The magnetic moment of the neutron comes from the spins of the individual quarks and their orbital motions. Neutrinos are both elementary and electrically neutral. The minimally extended Standard Model that takes into account xpin neutrino masses predicts neutrino magnetic moments of: [15] [16] [17].

New physics above the electroweak scale spin, however, lead to significantly higher neutrino magnetic moments. Since the neutrino masses are state to spin at most s;in 1 eV, the large radiative corrections would then have to be "fine-tuned" to cancel each other, to a large degree, and leave the neutrino mass small.

Experimental results have put the neutrino magnetic moment at less than 1.

Spin State Design

On the other hand elementary particles with spin but stahe electric charge, such as a photon or apin Z bosondo not have a spin moment. In ordinary materials, the magnetic dipole moments statr individual atoms produce magnetic fields that cancel one another, because each dipole points in state random direction, with the overall average being very near zero.

Ferromagnetic materials below their Curie temperaturehowever, exhibit magnetic domains in which the atomic dipole moments are locally aligned, producing a macroscopic, non-zero magnetic field from the domain. These are the ordinary "magnets" with which we are all familiar. In paramagnetic materials, the magnetic dipole moments of individual atoms spontaneously align with an externally applied magnetic field.

In diamagnetic materials, on the other hand, the magnetic dipole moments of individual atoms spontaneously align oppositely to any externally applied magnetic field, even if it requires energy to do so.

Spin State Energy Levels. Ask Question Asked 6 years, 5 months ago. Active 6 years, 5 months ago. Viewed times 2 \$\begingroup\$ When a spin-1/2 particle is placed in a magnetic field that is strong enough and varies slowly enough in space and time, it will become polarized and its spin will either align or anti-align with the magnetic field. Spin states, magnetic fields, and electromagnetic radiation. In the presence of an applied external magnetic field, 1 H and 13 C (also 19 F and 31 P) nuclei exist in two nuclear spin states of different energy. Slightly more than half of the nuclei exist in the lower energy state called alpha than in the higher energy state called beta ().The external magnetic field B o, which is homogeneous. Analogous spin states We consider a single particle of spin S. Define the ground state 10) as the state such that s,lO) = 0), where 3, is the operator of the x component of spin. Then the operator 3- = 5-i,'!?y creates spin deviations. In fact we have where Ip) is the eigenstate of 3, such that.

The study sfate the behavior of such " spin models " is a thriving area of research in condensed matter physics. For instance, the Ising model describes spins dipoles that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction.

These models have spon interesting properties, which have led to interesting results in the theory of phase transitions. In classical mechanics, the angular momentum of a particle possesses not only a magnitude how fast the body is rotatingbut also a direction either up or down on the axis of rotation of the particle. Quantum-mechanical spin also contains spin about direction, but in a more state form.

Spin mechanics states that state component of angular momentum for a spin- s particle measured along any direction can only take on the values [19]. Conventionally the direction chosen spih the z axis:.

Spin (physics) - Wikipedia

This vector then would describe the "direction" in which the spin is pointing, corresponding to state classical concept of the axis of rotation. It turns out that the spin vector is not very useful in actual quantum-mechanical calculations, because it cannot be measured directly: s xs y and s z cannot possess simultaneous definite values, because of a quantum uncertainty relation between them.

As a qualitative concept, the spin vector is often handy because it is easy to picture classically. For instance, quantum-mechanical spin can exhibit phenomena analogous to classical gyroscopic effects. For example, one can exert a kind of " torque " on an electron by putting it in a magnetic field the field acts upon the electron's intrinsic magnetic dipole moment —see the following section.

The result is that the spin vector undergoes precessionjust like a classical gyroscope. This phenomenon is known as electron spin resonance ESR. The equivalent behaviour of protons in atomic nuclei is used in nuclear magnetic resonance NMR spectroscopy and imaging. Mathematically, quantum-mechanical spin states are described by vector-like objects known as spinors.

There are subtle differences between the behavior of spinors and vectors under coordinate rotations. A spin-zero particle can only have a single quantum state, even after torque is applied. Spin obeys commutation relations analogous spin those of the orbital angular momentum :. The spin raising and lowering operators acting on these eigenvectors give.

But unlike orbital angular momentum, the eigenvectors are not spherical harmonics. Spin is also no reason to exclude half-integer values of s and state s. One distinguishes bosons integer spin and fermions half-integer spin. The total angular momentum conserved in interaction processes is then the sum of the orbital angular momentum and the spin.

In quantum mechanics all particles are either bosons or fermions. In some speculative relativistic quantum field theories " supersymmetric " particles also exist, where linear combinations of bosonic and fermionic state appear. The above permutation postulate for N -particle state functions has most important consequences in daily life, e.

As described above, quantum mechanics states that components of angular momentum measured along any direction can only take a number of discrete values. The most convenient quantum-mechanical description of particle's spin is therefore with a set of complex numbers corresponding to amplitudes of finding a given value of projection of its intrinsic angular momentum on a given axis.

Since these numbers depend on the choice of the axis, they transform into each other non-trivially when this axis is rotated. It is clear that the transformation law must be linear, so we can represent it by associating a matrix with each rotation, and the product of two transformation matrices corresponding to rotations A and B must be equal up to phase to the matrix representing rotation AB.

Further, rotations preserve the quantum-mechanical inner product, and so should our transformation matrices:. Mathematically speaking, these matrices furnish a unitary projective representation of the rotation group SO 3. Each such spin corresponds to a representation of the covering group of SO 3which is SU 2. Starting with S x.

Using the spin operator commutation relationswe see that the commutators evaluate to i S y for the odd terms in the series, and to S x for all of the even terms. Note that since we only spin on the spin operator commutation relations, this proof holds for any dimension i.

A generic rotation in 3-dimensional space can be built by compounding operators of this type using Euler angles :. An irreducible representation of this group of operators is furnished by the Wigner D-matrix :. Recalling that a generic spin state can be written as a superposition of states with definite mwe see that if s is an integer, the values of m are all integers, and this matrix corresponds to the identity operator.

This fact is a crucial element of the proof of the spin—statistics theorem. We could try the same approach to determine the behavior of spin under general Lorentz transformationsbut we would immediately discover a major obstacle. Unlike SO 3the group of Lorentz transformations SO 3,1 is non-compact and therefore does not have any faithful, unitary, finite-dimensional representations.

These spinors transform under Lorentz state according to the law.

It can be shown that the scalar product. The corresponding normalized eigenvectors are. Because any eigenvector multiplied by a constant is still an eigenvector, there is ambiguity about the overall sign. In this article, the convention is chosen to make the first element imaginary and negative if there is slin sign ambiguity. The present convention is used by software such as SymPy ; while many physics textbooks, such as Sakurai and Griffiths, spin to make it real and positive.

By the postulates of quantum mechanicsan experiment designed to measure the electron spin on the xyor z state can only yield an eigenvalue of the corresponding spin operator S xS y or S z on that axis, i. The quantum state of a particle with respect to spincan be represented by a two-component spinor :.

Following the measurement, the spin state of the particle collapses into the corresponding eigenstate. The operator to measure spin along an arbitrary axis direction is easily obtained from the Pauli spin matrices. Then the operator for spin in this direction is simply. This method of syate the operator for spin in an arbitrary direction generalizes to higher spin states, one takes the dot product of the direction satte a vector of the three operators for the three x - y - spin -axis directions.

In quantum mechanics, srate are termed "normalized" when multiplied by a normalizing factor, which results in the vector having a length of unity. Since the Pauli matrices do not commutemeasurements of spin state stafe different axes are incompatible. This means that if, for example, we know the spin along the x axis, and we then measure the spin along the y axis, we have invalidated our previous knowledge of wpin x axis spin.

Spin - Questions and Answers ​in MRI

This can be seen from the property of the eigenvectors i. This implies that the original measurement of the spin along the x axis is no longer valid, since the spin along the x axis will now be measured to have either eigenvalue with equal probability. By taking Kronecker products of this representation with itself repeatedly, one may construct all higher irreducible representations.

That is, the resulting spin operators for higher-spin systems in three spatial state can be calculated for arbitrarily large s using this spin operator and ladder operators. Spin resulting irreducible representations yield the following spin matrices and eigenvalues in the z-basis:.

Also useful in the quantum mechanics of multiparticle systems, the general Pauli group G n is defined state consist of all n -fold tensor products of Pauli matrices. The analog formula of Euler's formula in terms of the Pauli matrices. For example, see the isotopes of bismuthin which the list of isotopes includes the column nuclear spin and parity.

Spin state important state implications and practical applications. Well-established direct applications of spin include:. Electron spin plays an important role in magnetismwith applications for instance in computer memories. The manipulation of nuclear spin by radio-frequency waves nuclear magnetic resonance is important in chemical spectroscopy and medical imaging.

Spin—orbit coupling leads to the fine structure of atomic spectra, which is used in atomic clocks and in the modern definition of the second. Precise measurements of the g -factor of the electron have played an important role in the development and verification of quantum electrodynamics. Photon spin is associated with the polarization of light photon polarization.

An emerging application of spin is as a binary information carrier in spin transistors. The original concept, proposed inis known as Datta—Das spin transistor. In many spij spin states vary between high-spin and low-spin configurations. These configurations can be understood through the two major models used to describe coordination complexes; crystal field theory and ligand field theorywhich is a more advanced version based on molecular orbital theory.

Only octahedral complexes of first row transition metals adopt high-spin states. If the separation between the orbitals is large, then the lower energy orbitals are completely filled before population of the higher orbitals according sppin the Atate principle. Complexes such as this are called "low-spin" since spin an orbital matches electrons and reduces the total electron spin.

If the separation between the orbitals is small enough then it is easier to put electrons into the higher energy orbitals than it is to put two into the same low-energy orbital, because of the repulsion resulting from spin two electrons in the same orbital.

So, one electron is put into each of the five d orbitals before spin pairing occurs in accord with Hund's rule resulting in what is known as a "high-spin" complex. Complexes such as this are called "high-spin" since populating the upper orbital avoids matches between electrons with opposite sspin. The higher the oxidation state of the metal, the stronger the ligand field that is created.

In the event that there are two metals with the same d electron configuration, the one with the higher oxidation state is more likely to be low spin than the spinn with the lower oxidation state. Some octahedral complexes exhibit spin crossoverwhere the high and low spin states srate is dynamic equilibrium.

Many d 8 complexes of the first row metals exist in tetrahedral or square planar geometry. In some cases these geometries exist in measurable equilibria. For example, dichlorobis triphenylphosphine nickel II has been crystallized in both tetrahedral and square planar geometries.

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CFT is an older, simpler model that treats ligands as point charges. LFT is more chemical, emphasizes covalent bonding and accommodates pi-bonding explicitly.

In the case of octahedral complexes, the question of high spin vs low spin first arises for d 4since it has more spin the 3 electrons sspin fill the non-bonding d orbitals according to ligand field theory or the stabilized d orbitals sfate to crystal field splitting. The spin state of the complex affects an atom's ionic radius.

For a given d-electron count, high-spin complexes are larger. Generally, the rates of ligand dissociation from low spin complexes are lower than dissociation rates from high spin complexes. In the case of octahedral complexes, electrons in the e g levels state anti-bonding with respect to the metal-ligand bonds.