# Homework Help: What is the potential?

1. Aug 16, 2005

### eljose

let be the next problem: given a particle with mass so $$\hbar=(2m)^{0.5}$$ then we would have the quantum Hamiltonian:

$$H\phi(x)=E_{n}\phi(x)$$ with $$H=-D^{2}\phi+V(x)\phi$$

my question is how i would choose the potential so we have that the energies are the root of the equation $$f(x)=0$$

i try using the WKB approach to calculate the function:

$$\phi(x)=e^{iS(x)/\hbar}$$ with $$s^{2}=E_{n}-V(x)$$

with that i get a functional equation for the potential V(x), my problem is how i introduce the condition that the energies are the roots of f(x)...