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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.

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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

R2 v1 2026-06-22T08:15:51.126Z