Dual wavefunctions in two-dimensional quantum mechanics
Hojman
S
A
author
Asenjo
F
A
author
2020
English
It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefunctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to each other. This is a property of solutions with vanishing Bohm potential. These solutions can be extended to three-dimensional systems. We explicitly calculate dual solutions for physical systems, such as the repulsive harmonic oscillator and the two-dimensional hydrogen atom. These dual wavefunctions are also solutions of an analogue optical system in the eikonal limit. In this case, the potential is related to the refractive index, allowing the study of this two-dimensional dual wavefunction solutions with an optical (analogue) system. (C) 2020 Elsevier B.V. All rights reserved.
Schrodinger equation
Dual solution
Bohm potential
Two-dimensions
Optics
WOS:000525434900002
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text
10.1016/j.physleta.2020.126263
Hojman+Asenjo2020
Physics Letters A
Phys. Lett. A
2020
Elsevier
continuing
periodical
academic journal
384
13
5 pp
0375-9601