### Abstract

Original language | English |
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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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### Cite this

*Applied Mathematical Sciences*,

*9*(72), 3561-3567. https://doi.org/10.12988/ams.2015.53200

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*Applied Mathematical Sciences*, vol. 9, no. 72, pp. 3561-3567. https://doi.org/10.12988/ams.2015.53200

**Asymptotic evaluation of an integral arising in quantum harmonic oscillator tunnelling probabilities.** / Paris, R. B.

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 -