Quantum harmonic oscillator tunneling puzzle

[arkajad]

Avodyne: Please check the new file .
The paper is at the final stages. there is still an "anonymous helper" in the acknowledgments.

 

[arkajad]

Happy end of the story:

Asymptotic[/PLAIN] evaluation of an integral arising in quantum harmonic oscillator tunnelling probabilities

R B Paris

(Submitted on 11 Feb 2015)

 

[Derek Potter]

So would I be right in thinking that this is no longer a puzzle but just a slight surprise?

Actually I found the result a little surprising myself. I think it was because the probability density is a function of both x and n. I naturally expected an exponential dependence on x and I guess this spilled over to expecting a steep dependence on n as well. But as soon as I realized this, I started wondering whether there was any intuitive reason to expect it to fall off with n at all - it would not, AFAIK, go against any fundamental principle if the probability of finding a system outside of its classical range asymptotically approached some constant.

 

[arkajad]

The old problem of large quantum numbers and the correspondence principle is still being discussed. Cabrera and Kiwi, Large quantum-number states and the correspondence principle, Phys. Rev. A 36, 2995(R) September 1987 show how it can be violated for the harmonic oscillator.