The quartic anharmonic oscillator and its associated nonconstant magnetic field
- Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242 (United States)
Quantum mechanical anharmonic oscillators and Hamiltonians for particles in external magnetic fields are related to representations of nilpotent groups. Using this connection the eigenfunctions of the quartic anharmonic oscillator with potential V{sub {alpha}}(x)=({alpha}+(x{sup 2}/2)){sup 2} can be used to determine the eigenfunctions of a charged particle in a nonconstant magnetic field, of the form B{sub z}={beta}{sub 2}+{beta}{sub 3}x. The quartic anharmonic oscillator eigenvalues for low-lying states are obtained numerically and a function which interpolates between {alpha}{lt}0 (a double harmonic oscillator) and {alpha}{gt}0 (a harmonic oscillator) is shown to give a good fit to the numerical data. Approximate expressions for the quartic anharmonic oscillator eigenfunctions are then used to get the eigenfunctions for the magnetic field Hamiltonian. {copyright} {ital 1997 American Institute of Physics.}
- OSTI ID:
- 542572
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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