N-dimensional electron in an anharmonic potential

the large-N limit

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)108-111
Number of pages4
JournalPhysics Letters A
Volume357
Issue number2
Early online date27 Apr 2006
DOIs
Publication statusPublished - 4 Sep 2006

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energy levels
many body problem
eigenvectors
electrons
expansion

Keywords

  • 1 / N-expansion
  • hyperspherical coordinates

Cite this

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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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N-dimensional electron in an anharmonic potential : the large-N limit. / Chattopadhyay, Amit K.

In: Physics Letters A, Vol. 357, No. 2, 04.09.2006, p. 108-111.

Research output: Contribution to journalArticle

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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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