- #1

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## Homework Statement

Consider a particle which is confined in a one-dimensional box of size L, so that the position space wave function ψ(x) has to vanish at x = 0 and x = L. The energy operator is H = p

^{2}/2m + V (x), where the potential is V (x) = 0 for 0 < x < L, and V (x) = ∞ otherwise.

Find the position-space wave functions ψ

_{n}(x) ≡ <x|ψ

_{n}> of the energy eigenstates |ψ

_{n}>. Make sure that your wave functions are normalized, so that <ψ

_{n}|ψ

_{n}> = 1

## Homework Equations

maybe

<x'|x|ψ> = x'<x'|ψ>

1 =

## The Attempt at a Solution

I'm not 100% sure what the question is asking for but I'm guessing it's asking me to find the RHS of

ψ

_{n}(x) ≡ <x|ψ

_{n}>

I can write the RHS as a sum since energy eigenstates are discrete

<x|ψ

_{n}> = <x|1|ψ

_{n}> = ∑ψ

_{ni}

^{2}

I'm not sure if this is the right step but it's all I could come up with.