Bohr–Sommerfeld quantization

According to the Bohr–Sommerfeld quantization postulate the periodic motion of a particle in a potential field must satisfy the followint quantization rule:

\(\oint p dq = hn\)

\(p\) - is momentum of a particle

\(dq\) - is generalized coordinate of a particle

\(n\) - is a positive integer

Find the value of energy for unidimensional potential field \(U=\frac{kx^2}{2}\) at \(n=3\) state and

\(k=\frac{576\pi^2}{ h^2}\)



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