TY - JOUR

T1 - The biharmonic oscillator and asymmetric linear potentials

T2 - From classical trajectories to momentum-space probability densities in the extreme quantum limit

AU - Ruckle, L. J.

AU - Belloni, M.

AU - Robinett, R. W.

PY - 2012/11

Y1 - 2012/11

N2 - 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.

AB - 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.

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U2 - 10.1088/0143-0807/33/6/1505

DO - 10.1088/0143-0807/33/6/1505

M3 - Article

AN - SCOPUS:84866100525

VL - 33

SP - 1505

EP - 1525

JO - European Journal of Physics

JF - European Journal of Physics

SN - 0143-0807

IS - 6

ER -