dorsal/arxiv
View SchemaThe Quantum Mechanical Current of the Pauli Equation
| Authors | Marek Nowakowski |
|---|---|
| Categories | |
| ArXiv ID | physics/9807019 |
| URL | https://arxiv.org/abs/physics/9807019 |
| DOI | 10.1119/1.19149 |
| Journal | Am. J. Phys. 67 (1999) 916 |
Abstract
We argue that the process of constructing the quantum mechanical current of the Pauli equation by copying the line of arguments used in the spin-0 case, i.e. the Schr\"{o}dinger equation, is ambiguous. We show that a non-relativistic reduction of the relativistic Dirac four-vector current is, however, capable of fully resolving the problem. This analysis reveals that the non-relativistic current of the Pauli equation should include an extra term of the form $\vec \nabla \vec \times (\psi^{\dagger} \vec \sigma \psi)$. We present an initial exploration of the potential consequences of this new 'spin-term' by solving the Pauli equation for crossed magnetic and electric fields and calculating the corresponding current.
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"abstract": "We argue that the process of constructing the quantum mechanical current of\nthe Pauli equation by copying the line of arguments used in the spin-0 case,\ni.e. the Schr\\\"{o}dinger equation, is ambiguous. We show that a\nnon-relativistic reduction of the relativistic Dirac four-vector current is,\nhowever, capable of fully resolving the problem. This analysis reveals that the\nnon-relativistic current of the Pauli equation should include an extra term of\nthe form $\\vec \\nabla \\vec \\times (\\psi^{\\dagger} \\vec \\sigma \\psi)$. We\npresent an initial exploration of the potential consequences of this new\n\u0027spin-term\u0027 by solving the Pauli equation for crossed magnetic and electric\nfields and calculating the corresponding current.",
"arxiv_id": "physics/9807019",
"authors": [
"Marek Nowakowski"
],
"categories": [
"physics.ed-ph",
"quant-ph"
],
"doi": "10.1119/1.19149",
"journal_ref": "Am. J. Phys. 67 (1999) 916",
"title": "The Quantum Mechanical Current of the Pauli Equation",
"url": "https://arxiv.org/abs/physics/9807019"
},
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