Bohr - Sommerfeld quantization rules in the semiclassical limit

George A. Hagedorn, Sam L. Robinson

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We study one-dimensional quantum mechanical systems in the semiclassical limit. We construct a lowest order quasimode ψ(ℏ) for the Hamiltonian H(ℏ) when the energy E and Planck's constant ℏ satisfy the appropriate Bohr - Sommerfeld conditions. This means that ψ(ℏ) is an approximate solution of the Schrödinger equation in the sense that \\[H(ℏ) - E]ψ(ℏ)|| ≤ Cℏ3/2||ψ(ℏ)||. It follows that H(ℏ) has some spectrum within a distance Cℏ3/2 of E. Although the result has a long history, our time-dependent construction technique is novel and elementary.

Original languageEnglish (US)
Pages (from-to)10113-10129
Number of pages17
JournalJournal of Physics A: Mathematical and General
Issue number50
StatePublished - Dec 18 1998
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)


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