The biharmonic oscillator and asymmetric linear potentials: From classical trajectories to momentum-space probability densities in the extreme quantum limit

L. J. Ruckle, M. Belloni, R. W. Robinett

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The biharmonic oscillator and the asymmetric linear well are two confining power-law-type potentials for which complete bound-state solutions are possible in both classical and quantum mechanics. We examine these problems in detail, beginning with studies of their trajectories in position and momentum space, evaluation of the classical probability densities for both x and p, and calculation of the corresponding quantum-mechanical solutions which give |ψn(x)|2 and |n(p)|2 for comparison to their classical counterparts in theclassically allowed regions. We then focus on the behavior of n(p) for large momenta, motivated by recent studies of the very direct connections between the continuity behavior of V(x) and the large-p limit of the momentum-space wavefunction.

Original languageEnglish (US)
Pages (from-to)1505-1525
Number of pages21
JournalEuropean Journal of Physics
Volume33
Issue number6
DOIs
StatePublished - Nov 2012

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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