Search results
Results from the WOW.Com Content Network
The fact that the Pauli matrices, along with the identity matrix I, form an orthogonal basis for the Hilbert space of all 2 × 2 complex matrices , over , means that we can express any 2 × 2 complex matrix M as = + where c is a complex number, and a is a 3-component, complex vector.
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 ...
The term spin matrix refers to a number of matrices, ... Pauli matrices, also called the "Pauli spin matrices". Generalizations of Pauli matrices; Gamma matrices, ...
Multi-qubit Pauli matrices can be written as products of single-qubit Paulis on disjoint qubits. Alternatively, when it is clear from context, the tensor product symbol can be omitted, i.e. unsubscripted Pauli matrices written consecutively represents tensor product rather than matrix product. For example:
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.
Alternatively, the 's represent the square roots of the eigenvalues of the non-Hermitian matrix ~. [2] Note that each λ i {\displaystyle \lambda _{i}} is a non-negative real number. From the concurrence, the entanglement of formation can be calculated.
The operator S u has eigenvalues of ± ħ / 2 , just like the usual spin matrices. This method of finding the operator for spin in an arbitrary direction generalizes to higher spin states, one takes the dot product of the direction with a vector of the three operators for the three x-, y-, z-axis directions.
It is named after Wolfgang Pauli and Józef Lubański. [1] It describes the spin states of moving particles. [2] It is the generator of the little group of the Poincaré group, that is the maximal subgroup (with four generators) leaving the eigenvalues of the four-momentum vector P μ invariant. [3]