Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 3561-3567 |
| Number of pages | 7 |
| Journal | Applied Mathematical Sciences |
| Volume | 9 |
| Issue number | 72 |
| DOIs | |
| Publication status | Published - 27 Apr 2015 |
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Asymptotic evaluation of an integral arising in quantum harmonic oscillator tunnelling probabilities. / Paris, R. B.
In: Applied Mathematical Sciences, Vol. 9, No. 72, 27.04.2015, p. 3561-3567.Research output: Contribution to journal › Article
TY - JOUR
T1 - Asymptotic evaluation of an integral arising in quantum harmonic oscillator tunnelling probabilities
AU - Paris, R. B.
PY - 2015/4/27
Y1 - 2015/4/27
N2 - 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.
AB - 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.
U2 - 10.12988/ams.2015.53200
DO - 10.12988/ams.2015.53200
M3 - Article
VL - 9
SP - 3561
EP - 3567
JO - Applied Mathematical Sciences
JF - Applied Mathematical Sciences
SN - 1314-7552
IS - 72
ER -