dorsal/arxiv
View SchemaTheorem of Levinson Via The Spectral Density
| Authors | L. J. Boya, J. Casahorran |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502133 |
| URL | https://arxiv.org/abs/quant-ph/0502133 |
Abstract
We deduce Levinson\'{}s theorem in non-relativistic quantum mechanics in one dimension as a sum rule for the spectral density constructed from asymptotic data. We assume a self-adjoint hamiltonian which guarantees completeness; the potential needs not to be isotropic and a zero-energy resonance is automatically taken into account. Peculiarities of this one-dimension case are explained because of the ``critical'' character of the free case $u(x) = 0$, in the sense that any atractive potential forms at least a bound state. We believe this method is more general and direct than the usual one in which one proves the theorem first for single wave modes and performs analytical continuation.
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"abstract": "We deduce Levinson\\\u0027{}s theorem in non-relativistic quantum mechanics in one\ndimension as a sum rule for the spectral density constructed from asymptotic\ndata. We assume a self-adjoint hamiltonian which guarantees completeness; the\npotential needs not to be isotropic and a zero-energy resonance is\nautomatically taken into account. Peculiarities of this one-dimension case are\nexplained because of the ``critical\u0027\u0027 character of the free case $u(x) = 0$, in\nthe sense that any atractive potential forms at least a bound state. We believe\nthis method is more general and direct than the usual one in which one proves\nthe theorem first for single wave modes and performs analytical continuation.",
"arxiv_id": "quant-ph/0502133",
"authors": [
"L. J. Boya",
"J. Casahorran"
],
"categories": [
"quant-ph"
],
"title": "Theorem of Levinson Via The Spectral Density",
"url": "https://arxiv.org/abs/quant-ph/0502133"
},
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