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## Homework Statement

Okay, so i have a wave function from a particle in an infinite square well that has an initiate wave function with an even mixture of the first two stationary states.

ψ(x,0) = A[ψ

_{1}(x) + ψ

_{2}(x)]

a. Normalize ψ(x,0)

b Find ψ(x,t) and |ψ(x,t)|

^{2}(use

**Euler's formula**e

^{itheta}= cos(theta) + isin(theta) to elimiate all exponentials from the equation.) let ω= pi

^{2}hbar/2ma

^{2}and we know e

_{n}= hbarn

^{2}ω

(there are K parts to the actually problem, but after these two i should be able to solve the rest myself)

## Homework Equations

Eulers equation as stated in the question, as well as the solved first two stationary states of a particle in an infite square well (SQRT(2/L)*Sin(npi/L*X) which can be substituted in for ψ

_{n}.

## The Attempt at a Solution

Okay so i know to normalize an equation i need to set it equal to one, square it and integrate from negative to positive infinity. However, i can also integrate from 0 to L in this case.

So i square it (use X for the first state, Y for the second state)

1 = A

^{2}∫2/L(X

^{2}+xy+y

^{2}) from 0 to L

So i dnt know how to do that integral, but Wolfram alpha does and spits out "2" which im kind of dubious on, anyone know if im going in the right direction?