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ERIC Number: EJ827967
Record Type: Journal
Publication Date: 2007-Jan
Pages: 13
Abstractor: As Provided
Reference Count: 11
ISBN: N/A
ISSN: ISSN-0143-0807
Particle in a Uniform Magnetic Field Under the Symmetric Gauge: The Eigenfunctions and the Time Evolution of Wave Packets
de Brito, P. E.; Nazareno, H. N.
European Journal of Physics, v28 n1 p9-21 Jan 2007
In the present work we treat the problem of a particle in a uniform magnetic field along the symmetric gauge, so chosen since the wavefunctions present the required cylindrical symmetry. It is our understanding that by means of this work we can make a contribution to the teaching of the present subject, as well as encourage students to use computer algebra systems in solving problems of quantum mechanics. We obtained the degeneracy of the spectrum of eigenvalues in a very clear way. Through the use of a computer algebra system we show graphs of the probability density associated with different eigenvalues as well as compare such functions for some degenerate states, which helps us to visualize the physics of the problem. We also present a semiclassical model which gives a physical insight regarding the paradoxical fact that eigenfunctions associated with opposite angular momenta and different energy eigenvalues have the same probability density. Finally, by solving the time-dependent Schrodinger equation we obtain the time evolution of a wave packet that at time zero was considered to be localized in a definite region of the lattice. The centroid of such a packet performs an orbit similar to that obtained in the classical treatment of a particle in a magnetic field. (Contains 9 figures.)
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
Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A