# Average position in the Morse potential

Does anyone know the analytical expression for $$\langleψ_n|x|ψ_n\rangle$$ in the Morse potential?

In other words, I'd like to find the average position of a particle at the $$n$$-th vibrational level in a Morse well.

• If you're just looking for the expression, it's readily available on the Wikipedia entry. If you're looking for more, please edit your question with additional information. – Kyle Kanos Aug 22 at 19:41
• @KyleKanos It gives the matrix element for $m>n$. – G. Smith Aug 22 at 22:01
• This paper has the result for $n=0$. – G. Smith Aug 22 at 22:09
• This paper might be relevant. I can’t tell because it is behind a paywall. – G. Smith Aug 22 at 22:12
• @G.Smith thanks! The second paper has serial expansions to calculate it with not-so-bad accuracy. I'll try to make it looking good and then put here as an answer. The first paper is also nice to have, since it's the simple expression which covers the most important case. – Karen Fidanyan Aug 23 at 13:55