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2009•arXiv (Cornell University)Open access

Harmonic oscillator in a one-dimensional box

Paolo Amore, Francisco Marcelo Fernández

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Abstract

We study a harmonic molecule confined to a one--dimensional box with impenetrable walls. We explicitly consider the symmetry of the problem for the cases of different and equal masses. We propose suitable variational functions and compare the approximate energies given by the variation method and perturbation theory with accurate numerical ones for a wide range of values of the box length. We analyze the limits of small and large box size.

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What this paper is about

We study a harmonic molecule confined to a one--dimensional box with impenetrable walls. We explicitly consider the symmetry of the problem for the cases of different and equal masses. We propose suitable variational functions and compare the approximate energies given by the variation method and perturbation theory with accurate numerical ones for a wide range of values of the box length. We analyze the limits of small and large box size.

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Available abstract

We study a harmonic molecule confined to a one--dimensional box with impenetrable walls. We explicitly consider the symmetry of the problem for the cases of different and equal masses. We propose suitable variational functions and compare the approximate energies given by the variation method and perturbation theory with accurate numerical ones for a wide range of values of the box length. We analyze the limits of small and large box size.

Key concepts: Perturbation (astronomy), Harmonic oscillator, Range (aeronautics), Perturbation theory (quantum mechanics), Symmetry (geometry), Harmonic, Physics, Statistical physics

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