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

R. B. Paris

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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
Issue number72
Publication statusPublished - 27 Apr 2015


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