Volume 36, Number 2, October II 1996
|Page(s)||81 - 86|
|Published online||01 September 2002|
Approximation procedure for an anharmonic oscillator with cubic and quartic terms
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
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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