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[ψ1(x) + ψ2(x)]
a. Normalize ψ(x,0)
b Find ψ(x,t) and |ψ(x,t)|2 (use Euler's formula eitheta = cos(theta) + isin(theta) to elimiate all exponentials from the equation.) let ω= pi2hbar/2ma2 and we know en = hbarn2ω
(there are K parts to the actually problem, but after these two i should be able to solve the rest myself)
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 ψn.
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 = A2 ∫2/L(X2+xy+y2) 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?