### Abstract

The quantum dynamics of a free particle on a circle with point interaction is described by a U(2) family of self-adjoint Hamiltonians. We provide a classification of the family by introducing a number of subfamilies and thereby analyze the spectral structure in detail. We find that the spectrum depends on a subset of U(2) parameters rather than the entire U(2) needed for the Hamiltonians, and that in particular there exists a subfamily in U(2) where the spectrum becomes parameter-independent. We also show that, in some specific cases, the WKB semiclassical approximation becomes exact (modulo phases) for the system. (C) 2000 Published by Elsevier Science B.V.

Original language | English |
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Pages (from-to) | 366-374 |

Number of pages | 9 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 264 |

Issue number | 5 |

DOIs | |

Publication status | Published - Jan 3 2000 |

### Fingerprint

### Keywords

- Point interaction
- Self-adjoint extension
- WKB approximation

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*264*(5), 366-374. https://doi.org/10.1016/S0375-9601(99)00850-6

**A free particle on a circle with point interaction.** / Fülöp, Tamás; Tsutsui, Izumi.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 264, no. 5, pp. 366-374. https://doi.org/10.1016/S0375-9601(99)00850-6

}

TY - JOUR

T1 - A free particle on a circle with point interaction

AU - Fülöp, Tamás

AU - Tsutsui, Izumi

PY - 2000/1/3

Y1 - 2000/1/3

N2 - The quantum dynamics of a free particle on a circle with point interaction is described by a U(2) family of self-adjoint Hamiltonians. We provide a classification of the family by introducing a number of subfamilies and thereby analyze the spectral structure in detail. We find that the spectrum depends on a subset of U(2) parameters rather than the entire U(2) needed for the Hamiltonians, and that in particular there exists a subfamily in U(2) where the spectrum becomes parameter-independent. We also show that, in some specific cases, the WKB semiclassical approximation becomes exact (modulo phases) for the system. (C) 2000 Published by Elsevier Science B.V.

AB - The quantum dynamics of a free particle on a circle with point interaction is described by a U(2) family of self-adjoint Hamiltonians. We provide a classification of the family by introducing a number of subfamilies and thereby analyze the spectral structure in detail. We find that the spectrum depends on a subset of U(2) parameters rather than the entire U(2) needed for the Hamiltonians, and that in particular there exists a subfamily in U(2) where the spectrum becomes parameter-independent. We also show that, in some specific cases, the WKB semiclassical approximation becomes exact (modulo phases) for the system. (C) 2000 Published by Elsevier Science B.V.

KW - Point interaction

KW - Self-adjoint extension

KW - WKB approximation

UR - http://www.scopus.com/inward/record.url?scp=0034598267&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034598267&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(99)00850-6

DO - 10.1016/S0375-9601(99)00850-6

M3 - Article

VL - 264

SP - 366

EP - 374

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 5

ER -