This one is from Liboff(p6.8)(adsbygoogle = window.adsbygoogle || []).push({});

Given the wavefunction:

[tex]\psi(x, t) = A exp[i(ax - bt)][/tex]

What is the Potential field V(x) in which the particle is moving?

If the momentum of the particle is measured, what value is found(in terms of a & b)?

If the energy is measured, what value is found?

My Work:

[tex]\psi(x, t) = A exp[i(ax - bt)][/tex]

I took the partial derivatives wrt to t and x:

[tex]\frac{\partial \psi}{\partial t} = -(ib)\psi[/tex]

[tex]\frac{\partial^2 \psi}{\partial x^2} = -a^2\psi[/tex]

Time dependent Schrodinger's equation is:

[tex]i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m}\frac{\partial^2 \psi}{\partial x^2} + V(x)\psi[/tex]

Substituting the above values in this equation:

[tex]\hbar b \psi = \frac{\hbar^2 a^2}{2m}\psi + V(x)\psi[/tex]

Dividing throughout by [itex]\psi[/itex] and rearranging, I get the potential field as:

[tex]V(x) = \hbar\left(b - \frac{\hbar a^2}{2m}\right)[/tex]

Am I going right? Before I can proceed furthur...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding the Potential

**Physics Forums | Science Articles, Homework Help, Discussion**