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Perturbation theory for particle in a box

✍ Scribed by H. Kleinert; A. Chervyakov; B. Hamprecht

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
114 KB
Volume
260
Category
Article
ISSN
0375-9601

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✦ Synopsis

Recently developed strong-coupling theory opens 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 frequency term v, the ground-state energy E Ε½0. can be expanded perturbatively in powers of p 2 rv d 2 , where d is the box size. The removal of the infrared cutoff v requires the resummation of the series at an infinitely strong coupling. We show that strong-coupling theory yields a fast-convergent sequence of approximations to the well-known quantum-mechanical energy E Ε½0. s p 2 r2 d 2 .

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