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let be a non-smooth potential , for example a linear combination of step functions

$$ \sum_{n=0}^{10}H(x-n) $$

my question is, for this potential would be Bohr-sommerfeld quantization formula valid ??

is there any resource where they apply bohr sommerfeld formula to non-smooth potentials

$$ 2\pi (n+\frac{1}{2})\hbar = \oint _{C}p.dq $$

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Comment to the question(v1): OP's explicit example $V(x)=\sum_{n=0}^{10}H(x-n)$ does not have any bounded states (which would mean that the Bohr-Sommerfeld semiclassical quantization formula does not apply), unless one additionally imposes a lower bound for the $x$-coordinate. –  Qmechanic Nov 19 '12 at 16:33
    
er wel for exqample a potential that tends to infinity , like $ [x] $ with Dirichlet conditions at $ x=0 $ , or for example any potential like $ \sum_{n=0}^{\infty}H(x^{2}-n^{2}) $ –  Jose Javier Garcia Nov 19 '12 at 18:13

1 Answer 1

I believe it is valid without a continuity assumption, but (as always) only up to higher orders in $\hbar$.

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you mean piecewise continous function ??, for example like an step function or similar ??, –  Jose Javier Garcia Nov 19 '12 at 12:10
    
@JoseJavierGarcia: Yes. You can approximate it by a smooth function and then take a limit. –  Arnold Neumaier Nov 19 '12 at 14:34

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