Bohr - Sommerfeld quantization rules in the semiclassical limit

George A. Hagedorn, Sam L Robinson

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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
Volume31
Issue number50
DOIs
StatePublished - Dec 18 1998
Externally publishedYes

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Hamiltonians
Semiclassical Limit
Mechanical Systems
Quantum Systems
Lowest
Quantization
Approximate Solution
histories
Energy
energy
History

ASJC Scopus subject areas

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

Cite this

Bohr - Sommerfeld quantization rules in the semiclassical limit. / Hagedorn, George A.; Robinson, Sam L.

In: Journal of Physics A: Mathematical and General, Vol. 31, No. 50, 18.12.1998, p. 10113-10129.

Research output: Contribution to journalArticle

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