Answer to Question #140814 in Quantum Mechanics for Sneha

Question

Write down formula for energy in wkb method when potential is x^n.

Answer 1

Solution

If potential is n power of x or

$V=A x^n$

Then it's energy by using WKB method written as

$E=A\times\\((N-\frac{1}{2}) \hbar\sqrt\frac{\pi}{2m\alpha}\frac{\top(\frac{1}{n}+\frac{3}{2}) }{\top(\frac{1}{n}+1)})^{\frac{2n}{2+n}}$