Dual wavefunctions in two–dimensional quantum mechanics

Sergio A. Hojman, Felipe A. Asenjo

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


It is shown that the Schrödinger 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 Böhm 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.

Original languageEnglish
Article number126263
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number13
StatePublished - 7 May 2020


  • Bohm potential
  • Dual solution
  • Optics
  • Schrödinger equation
  • Two–dimensions


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