Convergent Perturbation Theory for a q-deformed Anharmonic Oscillator

Details Convergent Perturbation Theory for a q-deformed Anharmonic Oscillator Convergent Perturbation Theory for a q-deformed Anharmonic Oscillator

1998-08-05

arxiv.org/abs/math/9808024v1

Mathematics

Quantum Algebra

14 pages, 2 figure using epsf

Scientific paper

A $q$--deformed anharmonic oscillator is defined within the framework of
$q$--deformed quantum mechanics. It is shown that the Rayleigh--Schr\"odinger
perturbation series for the bounded spectrum converges to exact eigenstates and
eigenvalues, for $q$ close to 1. The radius of convergence becomes zero in the
undeformed limit.

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