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Perturbation Theory for Particle in a Box

H. Kleinert·A. Chervyakov·B. Hamprecht
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Abstract

Recently developed strong-coupling theory open up the possibility of treating quantum-mechanical systems with hard-wall potentials via perturbation theory. To test the power of this theory we study here the exactly solvable quantum mechanics of a point particle in a one-dimensional box. Introducing an auxiliary harmonic mass term $m$, the ground-state energy $E^{(0)$ can be expanded perturbatively in powers of $1/md$, where $d$ is the box size. The removal of the infrared cutoff $m$ requires the resummation of the series at infinitely strong coupling. We show that strong-coupling theory yields a fast-convergent sequence of approximations to the well-known quantum-mechanical energy $E^{(0)= π^2/2d^2$.

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H. Kleinert, A. Chervyakov, B. Hamprecht. 1999-06-16. Perturbation Theory for Particle in a Box. https://doi.org/10.1016/s0375-9601(99)00541-1

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