Open Access
March 2011 A closed form solution for quantum oscillator perturbations using Lie algebras
Clark Alexander
J. Phys. Math. 3: 1-12 (March 2011). DOI: 10.4303/jpm/P101201


We give a new solution to a well-known problem, that of computing perturbed eigenvalues for quantum oscillators. This article is nearly self contained and begins with all the necessary algebraic tools to make the subsequent calculations. We define a new family of Lie algebras relevant to making computations for perturbed (anharmonic) oscillators, and show that the only two formally closed solutions are indeed harmonic oscillators themselves. Through elementary combinatorics and noncanonical forms of well-known Lie algebras, we are able to obtain a fully closed form solution for perturbed eigenvalues to first order.


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Clark Alexander. "A closed form solution for quantum oscillator perturbations using Lie algebras." J. Phys. Math. 3 1 - 12, March 2011.


Published: March 2011
First available in Project Euclid: 22 September 2011

zbMATH: 1264.81168
Digital Object Identifier: 10.4303/jpm/P101201

Primary: 37K30 , 70G65 , 81Q05

Keywords: dynamical systems , ergodic theory , Hamiltonian systems , Infinite-dimensional systems , Klein-Gordon equation , Lie algebras , Lie-group , quantum theory , Schroedinger equation , symmetries

Rights: Copyright © 2011 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.3 • March 2011
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