Asymptotic evaluation of an integral arising in quantum harmonic oscillator tunnelling probabilities

R. B. Paris

    Research output: Contribution to journalArticlepeer-review

    82 Downloads (Pure)

    Abstract

    We obtain an asymptotic evaluation of the integral ʃ ∞ √2n+1 e−x2 H2 n (x) dx for n → ∞, where Hn(x) is the Hermite polynomial. This integral is used to determine the probability for the quantum harmonic oscillator in the nth energy eigenstate to tunnel into the classically forbidden region. Numerical results are given to illustrate the accuracy of the expansion.
    Original languageEnglish
    Pages (from-to)3561-3567
    Number of pages7
    JournalApplied Mathematical Sciences
    Volume9
    Issue number72
    DOIs
    Publication statusPublished - 27 Apr 2015

    Fingerprint Dive into the research topics of 'Asymptotic evaluation of an integral arising in quantum harmonic oscillator tunnelling probabilities'. Together they form a unique fingerprint.

    Cite this