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## Homework Statement

√[/B]A particle in an infinite square well has the initial wave function:

[itex]Ψ(x, 0) = A x ( a - x )[/itex]

a) Normalize Ψ(x, 0)

b) Compute <x>, <p>, and <H> at t = 0. (Note: you cannot get <p> by differentiating <x> because you only know <x> at one instance of time)

## Homework Equations

## The Attempt at a Solution

For part a, I figured out A = [itex]\sqrt{30 / a^5}[/itex]

I'm sort of confused for part b. For <x>, I set up the integral like this:

[itex]\int_{0}^{a}x Ψ(x, 0)^2 dx[/itex]

And got [itex]\frac{a^6 A^2}{60}[/itex], but I'm not sure if I got it right.

For <p> and <H>, I don't know how to set up these integrals. How would I set up these integrals? I don't need you to solve it for me, I just wanted to know how to set them up.

Thank you for reading and helping.