How do I normalize Ψ(x,0) for a particle in an infinite square well?

[maxbye3]

Homework Statement

Normalise Ψ(x,0) (use the fact that both ψ1 and ψ2 are stationary states).
Will this wave function be normalised at any later time, t > 0?

Homework Equations

A particle in an infinite square well of width a has as its initial wave function an even mixture of the first two stationary states,
Ψ(x, 0) = A(ψ1(x) + ψ2(x)) .

The Attempt at a Solution

I get the concept of normalisation I would integrate the square of A(ψ1(x) + ψ2(x)) between 0 and a and equate it to 1.
I am confused how to integrate ψ1(x) or ψ2(x).
I see that ψ(n)=(2/L)^0.5 sin(π/L)exp−i(n2π2 ̄h)/2mL2)t
does the exponential term cancel when I square the complex conjugate?Anyway any help would be deeply appreciated, thanks.

 

[Jhero]

Hello,
Yes, you are correct in your approach to normalising the wave function. To integrate ψ1(x) or ψ2(x), you can use the fact that they are both stationary states, meaning they do not change with time. This allows you to treat them as constants when integrating.
As for your question about the exponential term, when you take the complex conjugate and square it, the exponential term will become positive, so it will not cancel out. However, when you integrate over time, the exponential term will still cancel out because it will have a factor of e^(-iEn t/ħ) and e^(iEn t/ħ), which will cancel each other out.
I hope this helps. Let me know if you have any other questions.