Asymptotic formula for quantum harmonic oscillator tunneling probabilities

Abstract

Using simple methods of asymptotic analysis it is shown that for a quantum harmonic oscillator in n-th energy eigenstate the probability of tunneling into the classically forbidden region obeys an unexpected but simple asymptotic formula: the leading term is inversely proportional to the cube root of n.

arXiv commentv6 13 pages, 6 figures, Several misprints corrected, added explanation of the origin of the second order correction. Submitted to Rep. Math. Phys