Generalised quantum anharmonic oscillator using an operator ordering approach

2002/06/02 by Anirban Pathak, Pathak, Anirban
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA

paper · pdf · doi:10.48550/arxiv.math-ph/0206001

9 pages, latex 2e, no figure Journal Reference: J. Phys. A 33 (2000) 5607-5613

arxiv created 2002/06/02 · arxiv updated 2009/11/30

Abstract

We construct a generalised expression for the normal ordering of (a+a^†)^m for integral values of m and use the result to study the quantum anharmonic oscillator problem in the Heisenberg approach. In particular, we derive generalised expressions for energy eigen values and frequency shifts for the Hamiltonian H=\fracx²2+\fracx²2+\fracλmx^m. We also derive a closed form first order multi scale perturbation theoretic operator solution of this Hamiltonian with a view to generalise some recent results of Bender and Bettencourt .

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