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## Homework Statement

Consider the wavefunction [itex]\Psi (x,t)=c_1 \psi _1 (x)e^{-\frac{iE_1t}{\hbar}}+c_2 \psi _2 (x)e^{-\frac{iE_2t}{\hbar}}[/itex] where [itex]\psi _1 (x)[/itex] and [itex]\psi _2 (x)[/itex] are normalized and orthogonal. Knowing [itex]\Psi (x,0)[/itex], find the values of [itex]c_1[/itex] and [itex]c_2[/itex].

## Homework Equations

[itex]C^2 \int _{-\infty}^{\infty} |\Psi (x,t)|^2 dx=1[/itex]. I also know that the product of psi 1 by psi 2 is worth 0 (they are orthogonal) so this simplifies the expression to integrate.

But I'm still left with the integration of both lower case psi functions that I don't know how to handle.

## The Attempt at a Solution

I'm thinking on how to use the fact that I know Psi at t=0 but so far I'm out of ideas.