Finding Potential Energy of a Particle in a Region of Space

[Tony11235]

In a region of space, a particle has a wave function given by $$\psi(x) = A\exp(\frac{-x^2}{2L^2}})$$ and energy $$E = \frac{\hbar^2}{2mL^2}$$

Find the potential energy as a function of x.

Do I plug these into the time independent wave equation and solve for U(x) ? If so, I don't see what exactly I'm supposed to do with the energy, E. There is already a similar term in the wave equation.

 

[topsquark]

In a region of space, a particle has a wave function given by $$\psi(x) = A\exp(\frac{-x^2}{2L^2}})$$ and energy $$E = \frac{\hbar^2}{2mL^2}$$

Find the potential energy as a function of x.

Do I plug these into the time independent wave equation and solve for U(x) ? If so, I don't see what exactly I'm supposed to do with the energy, E. There is already a similar term in the wave equation.

$$-\frac{\hbar^2}{2m}\frac{d^2}{dx^2} \psi(x) + U(x) \psi (x) = E \psi(x)$$.
Plug in what you know, take the derivative and solve for U(x).

-Dan

 

[Tony11235]

Ok I was thinking of the time-dependent wave equation.