dorsal/arxiv
View SchemaQuantum Tunneling and Caustics under Inverse Square Potential
| Authors | Hitoshi Miyazaki, Izumi Tsutsui |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0202037 |
| URL | https://arxiv.org/abs/quant-ph/0202037 |
| DOI | 10.1006/aphy.2002.6265 |
Abstract
Quantization of a harmonic oscillator with inverse square potential $V(x)=(m{\omega^2}/2){x^2}+g/{x^2}$ on the line $-\infty<x<\infty$ is re-examined. It is shown that, for $0<g<3{\hbar^2}/(8m)$, the system admits a U(2) family of inequivalent quantizations allowing for quantum tunneling through the potenatial barrier at $x=0$. In the family is a distinguished quantization which reduces smoothly to the harmonic oscillator as $g\to 0$, in contrast to the conventional quantization applied to the Calogero model which prohibits the tunneling and has no such limit. The tunneling renders the classical caustics anomalous at the quantum level, leading to the possibility of copying an arbitrary state from one side $x>0$, say, to the other $x<0$.
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"abstract": "Quantization of a harmonic oscillator with inverse square potential\n$V(x)=(m{\\omega^2}/2){x^2}+g/{x^2}$ on the line $-\\infty\u003cx\u003c\\infty$ is\nre-examined. It is shown that, for $0\u003cg\u003c3{\\hbar^2}/(8m)$, the system admits a\nU(2) family of inequivalent quantizations allowing for quantum tunneling\nthrough the potenatial barrier at $x=0$. In the family is a distinguished\nquantization which reduces smoothly to the harmonic oscillator as $g\\to 0$, in\ncontrast to the conventional quantization applied to the Calogero model which\nprohibits the tunneling and has no such limit. The tunneling renders the\nclassical caustics anomalous at the quantum level, leading to the possibility\nof copying an arbitrary state from one side $x\u003e0$, say, to the other $x\u003c0$.",
"arxiv_id": "quant-ph/0202037",
"authors": [
"Hitoshi Miyazaki",
"Izumi Tsutsui"
],
"categories": [
"quant-ph"
],
"doi": "10.1006/aphy.2002.6265",
"title": "Quantum Tunneling and Caustics under Inverse Square Potential",
"url": "https://arxiv.org/abs/quant-ph/0202037"
},
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