Asymptotic formula for quantum harmonic oscillator tunneling probabilities
Quantum Physics
2016-01-20 v6
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.
Cite
@article{arxiv.1501.07483,
title = {Asymptotic formula for quantum harmonic oscillator tunneling probabilities},
author = {Arkadiusz Jadczyk},
journal= {arXiv preprint arXiv:1501.07483},
year = {2016}
}
Comments
v6 13 pages, 6 figures, Several misprints corrected, added explanation of the origin of the second order correction. Submitted to Rep. Math. Phys