dorsal/arxiv
View SchemaDerivation of Spin Vectors and Operators From First Principles
| Authors | Habatwa Vincent Mweene |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9905012 |
| URL | https://arxiv.org/abs/quant-ph/9905012 |
Abstract
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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"date_created": "2026-03-02T18:02:48.351000Z",
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"abstract": "The interpretation of quantum mechanics due to Lande\u0027 is applied to the\nconnection between wave mechanics and matrix mechanics. The connection between\nthe differential eigenvalue equation and the matrix eigenvalue equation for an\noperator is elucidated. In particular, we show that the elements of a matrix\nvector state are probability amplitudes with a structure rather than being mere\nconstants. We obtain the most general expressions for the probability\namplitudes for the description of spin-1/2 measurements. As a result, we derive\nspin-1/2 operators and vectors from first principles. The procedure used is\nanalogous to that by which orbital angular momentum wavefunctions and operators\nare transformed to matrix mechanics vectors and matrices. The most generalized\nforms of the spin operators and their eigenvectors for spin-1/2 are derived and\nshown to reduce to the Pauli spin matrices and vectors in an appropriate limit.",
"arxiv_id": "quant-ph/9905012",
"authors": [
"Habatwa Vincent Mweene"
],
"categories": [
"quant-ph"
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"title": "Derivation of Spin Vectors and Operators From First Principles",
"url": "https://arxiv.org/abs/quant-ph/9905012"
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