* Time evolution of superposition (10 min)

a) What is the time evolution of an arbitrary wave function $\Psi(x,t=0)$,

$$\Psi(x,t=0)=\sum_{n=0}^{\infty}c_n\psi_n(x),\quad c_n=\int_0^Ldx \psi^*_n(x)\Psi(x)?$$ (11)

b) Consider the wave function

$$\Psi(x,t=0)=\frac{1}{\sqrt{2}}\left( \psi_1(x)+\psi_2(x) \right).$$ (12)

What is the probability density to find the particle at $x$ at time $t$?