- #1
Yoni V
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Homework Statement
Assume a particle with a wave function ##\psi(x)## such that ##-\infty < x < \infty##, that move under some potential ##V(x)##.
Show that:
a) two wave functions with same energies can only differ by a complex phase;
b) if the potential is real, then you can choose the wave function to be real as well;
c) the wave function of the ground state (with real potential) doesn't change sign.
Homework Equations
a) Schrodinger's time independent equation.
The Attempt at a Solution
I'm stuck at (a). Need a push in the right direction for the very start.
I want to show that if two wave functions ## \psi_1, \psi_2## satisfy
$$ \psi_{1/2}''(x) + \frac{2m}{\hbar^2}\left(E-V(x)\right)\psi_{1/2}(x)=0$$
then I can find an equation that ties them in a phase relation.
But aside from writing this statement down, I don't know how to proceed. Thanks.