Position wave function of energy eigenstates in 1D box

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 = p2/2m + V (x), where the potential is V (x) = 0 for 0 < x < L, and V (x) = ∞ otherwise.

Find the position-space wave functions ψn(x) ≡ <x|ψn> of the energy eigenstates |ψn>. Make sure that your wave functions are normalized, so that <ψnn> = 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

ψn(x) ≡ <x|ψn>

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

<x|ψn> = <x|1|ψn> = ∑ψni2

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

Chandra Prayaga
Are you familiar with the Schrodinger equation for such a system?

Are you familiar with the Schrodinger equation for such a system?

Yes, for a mass moving in 1D, the Schrodinger equation gives

n(x) + Vψn(x) = Eψn(x)

H = Hamiltonian

So if I solve the equation for a 1D box I would get something like

ψn(x) = Asin(kx)+Bsin(kx)

Do I then solve for k,A, and B?

I am unsure of what it means by position wave functions of energy eigenstates. Does it mean Solve for ψn(x) for the definite levels of energy levels?

BvU