dorsal/arxiv
View SchemaPT-Symmetric Cubic Anharmonic Oscillator as a Physical Model
| Authors | Ali Mostafazadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411137 |
| URL | https://arxiv.org/abs/quant-ph/0411137 |
| DOI | 10.1088/0305-4470/38/29/010 |
| Journal | J.Phys.A38:6557-6570,2005; Erratum-ibid.A38:8185,2005 |
Abstract
We perform a perturbative calculation of the physical observables, in particular pseudo-Hermitian position and momentum operators, the equivalent Hermitian Hamiltonian operator, and the classical Hamiltonian for the PT-symmetric cubic anharmonic oscillator, $ H=p^1/(2m)+\mu^2x^2/2+i\epsilon x^3 $. Ignoring terms of order $ \epsilon^4 $ and higher, we show that this system describes an ordinary quartic anharmonic oscillator with a position-dependent mass and real and positive coupling constants. This observation elucidates the classical origin of the reality and positivity of the energy spectrum. We also discuss the quantum-classical correspondence for this PT-symmetric system, compute the associated conserved probability density, and comment on the issue of factor-ordering in the pseudo-Hermitian canonical quantization of the underlying classical system.
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"abstract": "We perform a perturbative calculation of the physical observables, in\nparticular pseudo-Hermitian position and momentum operators, the equivalent\nHermitian Hamiltonian operator, and the classical Hamiltonian for the\nPT-symmetric cubic anharmonic oscillator, $ H=p^1/(2m)+\\mu^2x^2/2+i\\epsilon x^3\n$. Ignoring terms of order $ \\epsilon^4 $ and higher, we show that this system\ndescribes an ordinary quartic anharmonic oscillator with a position-dependent\nmass and real and positive coupling constants. This observation elucidates the\nclassical origin of the reality and positivity of the energy spectrum. We also\ndiscuss the quantum-classical correspondence for this PT-symmetric system,\ncompute the associated conserved probability density, and comment on the issue\nof factor-ordering in the pseudo-Hermitian canonical quantization of the\nunderlying classical system.",
"arxiv_id": "quant-ph/0411137",
"authors": [
"Ali Mostafazadeh"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1088/0305-4470/38/29/010",
"journal_ref": "J.Phys.A38:6557-6570,2005; Erratum-ibid.A38:8185,2005",
"title": "PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model",
"url": "https://arxiv.org/abs/quant-ph/0411137"
},
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