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When spinors are used to describe the quantum states, the three spin operators (S x, S y, S z,) can be described by 2 × 2 matrices called the Pauli matrices whose eigenvalues are ± ħ / 2 . For example, the spin projection operator S z affects a measurement of the spin in the z direction.
The number of operators is arbitrary, and they do not have to satisfy any special properties. But if the system is -dimensional, it can be shown [1] that the master equation can be fully described by a set of operators, provided they form a basis for the space of operators.
That is, the resulting spin operators for higher-spin systems in three spatial dimensions can be calculated for arbitrarily large s using this spin operator and ladder operators. For example, taking the Kronecker product of two spin- 1 / 2 yields a four-dimensional representation, which is separable into a 3-dimensional spin-1 ( triplet ...
The Ehrenfest theorem, named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position and momentum operators x and p to the expectation value of the force = ′ on a massive particle moving in a scalar potential (), [1]
The Jordan–Wigner transformation is a transformation that maps spin operators onto fermionic creation and annihilation operators.It was proposed by Pascual Jordan and Eugene Wigner [1] for one-dimensional lattice models, but now two-dimensional analogues of the transformation have also been created.
In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which ...
where are the values of the e.g. z-component of the spin in a spin chain, and the A s i are matrices of arbitrary dimension m. As m → ∞, the representation becomes exact. This theory was exposed by S. Rommer and S. Ostlund in .
All the operators (except typeof) listed exist in C++; the column "Included in C", states whether an operator is also present in C. Note that C does not support operator overloading. When not overloaded, for the operators && , || , and , (the comma operator ), there is a sequence point after the evaluation of the first operand.