Classical and Quantum Dispersion Relations

Sergio A. Hojman, Felipe A. Asenjo

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion relation, but they differ in the general case. The dispersion relations may also coincide when additional assumptions are made, such as WKB or eikonal approximations, for instance. This general result also holds for non-quantum wave equations derived from classical counterparts, such as in ray and wave optics, for instance. Explicit examples are given for covariant scalar, vectorial and tensorial fields in flat and curved spacetimes.

Original languageEnglish
Article number085001
JournalPhysica Scripta
Issue number8
StatePublished - Aug 2020


  • Bohm potential
  • Quantum Hamilton-Jacobi equation
  • dispersion relation


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