# Semiclassical Bohr quantization with a magnetic potential

1. Aug 20, 2010

### zetafunction

1. The problem statement, all variables and given/known data

given the Hamiltonian in one dimension $$H= \frac{(p-eA)^{2}}{2m}+ V(x)$$

use the Bohr-Sommerfeld quantization in one dimension to obtain n=n(E)

2. Relevant equations

Hamiltonian , quantization

3. The attempt at a solution

from the usual quantization algorithm in one dimension i get

$$\int_{0}^{a}dx (2m)^{1/2}(E-V(X))^{1/2}+ \int_{0}^{a}dxA(x) =nh$$

here 'a' is a turning point so V(a)=E , simply the contribution to n(E) by the magnetic potential is an integral of A(x)