N-dimensional electron in an anharmonic potential: the large-N limit

Amit K. Chattopadhyay

doi:10.1016/j.physleta.2006.04.028

N-dimensional electron in an anharmonic potential: the large-N limit

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Abstract

We show that the energy levels predicted by a frac(1, N)-expansion method for an N-dimensional electron in an anharmonic potential are always lower than the exact energy levels but monotonically converge toward their exact eigenstates for higher ordered corrections. The technique allows a systematic approach for quantum many body problems in a confined potential and explains the remarkable agreement of such approximate theories when compared with numerical results.

Original language	English
Pages (from-to)	108-111
Number of pages	4
Journal	Physics Letters A
Volume	357
Issue number	2
Early online date	27 Apr 2006
DOIs	https://doi.org/10.1016/j.physleta.2006.04.028
Publication status	Published - 4 Sept 2006

Keywords

1 / N-expansion
hyperspherical coordinates

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10.1016/j.physleta.2006.04.028

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abstract = "We show that the energy levels predicted by a frac(1, N)-expansion method for an N-dimensional electron in an anharmonic potential are always lower than the exact energy levels but monotonically converge toward their exact eigenstates for higher ordered corrections. The technique allows a systematic approach for quantum many body problems in a confined potential and explains the remarkable agreement of such approximate theories when compared with numerical results.",

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AB - We show that the energy levels predicted by a frac(1, N)-expansion method for an N-dimensional electron in an anharmonic potential are always lower than the exact energy levels but monotonically converge toward their exact eigenstates for higher ordered corrections. The technique allows a systematic approach for quantum many body problems in a confined potential and explains the remarkable agreement of such approximate theories when compared with numerical results.

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KW - hyperspherical coordinates

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JO - Physics Letters A

JF - Physics Letters A

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ER -

N-dimensional electron in an anharmonic potential: the large-N limit

Abstract

Keywords

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