Confined One Dimensional Harmonic Oscillator as a Two-Mode System

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The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in any ... continued below

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Gueorguiev, V G; Rau, A P & Draayer, J P July 11, 2005.

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The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in any other way. An alternative to casting the problem in terms of one or the other basis set consists of using an ''oblique'' basis that uses both sets. Through a study of this alternative in this one-dimensional problem, we are able to illustrate practical solutions and infer the applicability of the concept for more complex systems, such as in the study of complex nuclei where oblique-basis calculations have been successful.

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PDF-file: 13 pages; size: 0 Kbytes

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  • Journal Name: American Journal of Physics; Journal Volume: 74; Journal Issue: 5

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  • Report No.: UCRL-JRNL-213847
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 884759
  • Archival Resource Key: ark:/67531/metadc892012

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • July 11, 2005

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  • Sept. 23, 2016, 2:42 p.m.

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  • Nov. 23, 2016, 11:23 a.m.

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Gueorguiev, V G; Rau, A P & Draayer, J P. Confined One Dimensional Harmonic Oscillator as a Two-Mode System, article, July 11, 2005; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc892012/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.