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| related topics |
| {equation, function, exp} |
| {energy, state, states} |
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| {wave, scattering, interference} |
| {vol, operators, histories} |
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Unified treatment of the Coulomb and harmonic oscillator potentials in
$D$ dimensions
G. Lévai, B. Kónya, Z. Papp
abstract: Quantum mechanical models and practical calculations often rely on some
exactly solvable models like the Coulomb and the harmonic oscillator
potentials. The $D$ dimensional generalized Coulomb potential contains these
potentials as limiting cases, thus it establishes a continuous link between the
Coulomb and harmonic oscillator potentials in various dimensions. We present
results which are necessary for the utilization of this potential as a model
and practical reference problem for quantum mechanical calculations. We define
a Hilbert space basis, the generalized Coulomb-Sturmian basis, and calculate
the Green's operator on this basis and also present an SU(1,1) algebra
associated with it. We formulate the problem for the one-dimensional case too,
and point out that the complications arising due to the singularity of the
one-dimensional Coulomb problem can be avoided with the use of the generalized
Coulomb potential.
- oai_identifier:
- oai:arXiv.org:quant-ph/9802012
- categories:
- quant-ph
- comments:
- 18 pages, 3 ps figures, revtex
- arxiv_id:
- quant-ph/9802012
- journal_ref:
- J.Math.Phys. 39 (1998) 5811-5823
- created:
- 1998-02-03
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