Dual wavefunctions in two-dimensional quantum mechanics
arXiv:1910.11487 · doi:10.1016/j.physleta.2020.126263
Abstract
It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefuctions 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.
Cited by in corpus (7)
- Bohm potential is real and its effects are measurable
- Classical and Quantum Dispersion Relations
- Bohm potential for the time dependent harmonic oscillator
- Quantum particles that behave as free classical particles
- Bohm approach to the Gouy phase shift
- Engineering two-mode squeezed vacuum-like states by using the Bohm potential
- On the conditions for the classicality of a quantum particle