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Solution of the Quantum Harmonic Oscillator Plus a Delta-Function Potential at the Origin: The 'Oddness' of Its Even-Parity Solutions

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Title: Solution of the Quantum Harmonic Oscillator Plus a Delta-Function Potential at the Origin: The 'Oddness' of Its Even-Parity Solutions
Language: English
Authors: Viana-Gomes, J., Peres, N. M. R.
Source: European Journal of Physics. Sep 2011 32(5):1377-1384.
Availability: Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP
Peer Reviewed: Y
Physical Description: PDF
Page Count: 8
Publication Date: 2011
Document Type: Journal Articles
Reports - Descriptive
Descriptors: Textbooks, Quantum Mechanics, Calculus, Spreadsheets, Energy, Physics, Scientific Concepts, Equations (Mathematics), Computation, Science Education
DOI: 10.1088/0143-0807/32/5/025
ISSN: 0143-0807
Abstract: We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the boundary conditions at the origin. This problem calls the attention of the students to an inaccurate statement in quantum mechanics textbooks often found in the context of the solution of the harmonic oscillator problem. (Contains 1 table, 3 figures and 4 footnotes.)
Abstractor: As Provided
Number of References: 10
Entry Date: 2012
Accession Number: EJ963885
Database: ERIC
FullText Text:
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PubType: Academic Journal
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  Data: Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP
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  Data: We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the boundary conditions at the origin. This problem calls the attention of the students to an inaccurate statement in quantum mechanics textbooks often found in the context of the solution of the harmonic oscillator problem. (Contains 1 table, 3 figures and 4 footnotes.)
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