Exact quantization conditions

C. Rosenzweig, J. B. Krieger

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


The method of Froman and Froman for proving exact quantization conditions is reviewed. This formalism, unlike the usual WKB approximation to which it bears a close resemblance, requires consideration of the behavior of the potential everywhere it is defined. This approach leads to proofs that certain quantization conditions are exact without having to compare the results to solutions of the Schrödinger equation obtained by other means. Using the formalism, we prove the correctness of all previously known exact quantization rules for the one-dimensional and radial cases. Furthermore, it is shown that exact quantization rules can be proved for two other potentials. For one of these, no analytic solutions to the Schrödinger equation are known. For the latter case, the proof is checked by numerical integration of the Schrödinger equation for a special case.

Original languageEnglish (US)
Pages (from-to)849-860
Number of pages12
JournalJournal of Mathematical Physics
Issue number6
StatePublished - 1968
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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