The Bohr-Sommerfeld quantization condition for this problem is
Note that
defines
We may then rewrite the integral as
Let us now make the substitution,
We then obtain
or, evaluating the integral,
Solving for
we obtain
The energy spectrum is thus
If we now calculate the spacing between two adjacent energy levels, we obtain
We see that this spacing is indeed independent of mass (and, in fact, of
as well).
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