# h expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

## Abstract

We extend a theory of first order h corrections to Gutzwiller's trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform magnetic field. We exploit the C {sub 4v}-symmetry of the system in the calculation of the correction terms. The numerical results for the semiclassical values will be compared with values extracted from exact quantum mechanical calculations. The comparison shows an excellent agreement and demonstrates the power of the h expansion method.

- Authors:

- 1. Institut fuer Theoretische Physik, Universitaet Stuttgart, 70550 Stuttgart (Germany). E-mail: Holger.Cartarius@itp1.uni-stuttgart.de
- 1. Institut fuer Theoretische Physik, Universitaet Stuttgart, 70550 Stuttgart (Germany)

- Publication Date:

- OSTI Identifier:
- 20976727

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 2; Other Information: DOI: 10.1016/j.aop.2006.01.006; PII: S0003-4916(06)00026-1; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; HYDROGEN; MAGNETIC FIELDS; POTENTIALS; QUANTUM MECHANICS; SEMICLASSICAL APPROXIMATION; SYMMETRY; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Cartarius, Holger, Main, Joerg, and Wunner, Guenter.
```*h expansions in semiclassical theories for systems with smooth potentials and discrete symmetries*. United States: N. p., 2007.
Web. doi:10.1016/j.aop.2006.01.006.

```
Cartarius, Holger, Main, Joerg, & Wunner, Guenter.
```*h expansions in semiclassical theories for systems with smooth potentials and discrete symmetries*. United States. doi:10.1016/j.aop.2006.01.006.

```
Cartarius, Holger, Main, Joerg, and Wunner, Guenter. Thu .
"h expansions in semiclassical theories for systems with smooth potentials and discrete symmetries". United States.
doi:10.1016/j.aop.2006.01.006.
```

```
@article{osti_20976727,
```

title = {h expansions in semiclassical theories for systems with smooth potentials and discrete symmetries},

author = {Cartarius, Holger and Main, Joerg and Wunner, Guenter},

abstractNote = {We extend a theory of first order h corrections to Gutzwiller's trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform magnetic field. We exploit the C {sub 4v}-symmetry of the system in the calculation of the correction terms. The numerical results for the semiclassical values will be compared with values extracted from exact quantum mechanical calculations. The comparison shows an excellent agreement and demonstrates the power of the h expansion method.},

doi = {10.1016/j.aop.2006.01.006},

journal = {Annals of Physics (New York)},

number = 2,

volume = 322,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}

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