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The Casimir Energy in a Separable Potential

✍ Scribed by R.L. Jaffe; L.R. Williamson

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
167 KB
Volume
282
Category
Article
ISSN
0003-4916

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✦ Synopsis

The Casimir energy is the first-order-in-correction to the energy of a time-independent field configuration in a quantum field theory. We study the Casimir energy in a toy model, where the classical field is replaced by a separable potential. In this model the exact answer is trivial to compute, making it a good place to examine subtleties of the problem. We construct two traditional representations of the Casimir energy, one from the Green's function and the other from the phase shifts, and apply them to this case. We show that the two representations are correct and equivalent in this model. We study the convergence of the Born approximation to the Casimir energy and relate our findings to computational issues that arise in more realistic models.

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## Abstract If the local potential at each lattice site is replaced by a nonlocal projection operator, the eigenfunctions of the electrons can be eliminated from the SchrΓΆdinger equation. The method of Green's functions is utilized and calculation of the energy bands is done assuming projection pot