| Issue |
Europhys. Lett.
Volume 36, Number 2, October II 1996
|
|
|---|---|---|
| Page(s) | 81 - 86 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i1996-00190-3 | |
| Published online | 01 September 2002 | |
Approximation procedure for an anharmonic oscillator with cubic and quartic terms
1
Dipartimento di Fisica, Università di Roma I "La Sapienza”, P.le
A. Moro 5, 00185 Roma, Italy
2
INFN, Sezione di Roma 1, c/o Dipartimento di Fisica, Università
di Roma I "La Sapienza - P.le A. Moro 5, 00185 Roma, Italy
3
Dipartimento di Fisica, Università di Roma III "E. Amaldi”, Via
della Vasca Navale 84, 00146 Roma, Italy
4
Department of Physics, Theoretical Division, Lancaster University, Lancaster LA1 4YB,
England
Received:
1
July
1996
Accepted:
4
September
1996
We use — after a shift transformation of the variable — the Burrows, Cohen and Feldmann approximation procedure to solve the problem of finding the energy eigenvalues for an anharmonic oscillator with cubic and quartic terms subjected to a linear external potential. Both low- and high-frequency limits are considered. A first application is given by deriving (in the high-frequency case) the partition function of a gas composed of such anharmonic oscillators. We also exploit the recently proved formal equivalence between a high-frequency anharmonic oscillator (in the approximation considered) and an infinitesimally deformed harmonic oscillator to introduce SU(2) and SU(1,1) algebras for the anharmonic oscillator with cubic and quartic terms.
PACS: 02.60.Gf – Algorithms for functional approximation / 05.90.+m – Other topics in statistical physics and thermodynamics / 31.15.-p – Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations)
© EDP Sciences, 1996
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