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The term spin matrix refers to a number of matrices, which are related to Spin (physics). Quantum mechanics and pure mathematics.
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The analog formula to the above generalization of Euler's formula for Pauli matrices, the group element in terms of spin matrices, is tractable, but less simple. [7] Also useful in the quantum mechanics of multiparticle systems, the general Pauli group G n is defined to consist of all n-fold tensor products of Pauli matrices.
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Matrices for which this property holds are called orthogonal matrices. The group of all 3 × 3 orthogonal matrices is denoted O(3), and consists of all proper and improper rotations. In addition to preserving length, proper rotations must also preserve orientation.
Given a unit vector in 3 dimensions, for example (a, b, c), one takes a dot product with the Pauli spin matrices to obtain a spin matrix for spin in the direction of the unit vector. The eigenvectors of that spin matrix are the spinors for spin-1/2 oriented in the direction given by the vector. Example: u = (0.8, -0.6, 0) is a unit vector ...
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 states) and a 1-dimensional spin-0 representation (singlet state). The resulting irreducible representations yield the following spin matrices and eigenvalues in the z-basis:
Suppose there is a spin 1/2 particle in a state = [].To determine the probability of finding the particle in a spin up state, we simply multiply the state of the particle by the adjoint of the eigenspinor matrix representing spin up, and square the result.
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