Derivation of Spin Vectors and Operators From First Principles

Details Derivation of Spin Vectors and Operators From First Principles Derivation of Spin Vectors and Operators From First Principles

1999-05-05

arxiv.org/abs/quant-ph/9905012v2

Physics

Quantum Physics

LaTeX, 30 pages, submitted to "Foundations of Physics." Replaced to thoroughly revise notation and improve some sections

Scientific paper

The interpretation of quantum mechanics due to Lande' is applied to the connection between wave mechanics and matrix mechanics. The connection between the differential eigenvalue equation and the matrix eigenvalue equation for an operator is elucidated. In particular, we show that the elements of a matrix vector state are probability amplitudes with a structure rather than being mere constants. We obtain the most general expressions for the probability amplitudes for the description of spin-1/2 measurements. As a result, we derive spin-1/2 operators and vectors from first principles. The procedure used is analogous to that by which orbital angular momentum wavefunctions and operators are transformed to matrix mechanics vectors and matrices. The most generalized forms of the spin operators and their eigenvectors for spin-1/2 are derived and shown to reduce to the Pauli spin matrices and vectors in an appropriate limit.

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