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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.