# Infinite potential well energy question

1. Apr 15, 2012

### phys2

1. The problem statement, all variables and given/known data

A particle of mass m is confined (in one dimension) to the region 0 ≤ x ≤ a by a potential which is zero inside the region and infinitely large outside.

If the wavefunction at time t = 0 is of the form

ψ (x,0) = Ax(a - x) inside the region
ψ (x, 0) = 0 outside the region

(a) Find the value of A to normalise the wavefunction
(b) The probability of measuring the ground state energy of the particle.

2. Relevant equations

P = integral of ψ times its complex conjugate = 1

3. The attempt at a solution

So for (a), I used the formula above and integrating with respect to x from 0 to a, I got A = square root of 30/a5

(b) Since this is an infinite potential well, the energy values would be E = ħ2n2π2 / 2ma2 so the ground state energy would be ħ2π2 / 2ma2

So am I supposed to find the probability of getting the above ground state energy function?

I was thinking that this might have something to do with energy expectation values but then that has a dψ/dt under the integral so I would end up getting zero which wouldn't make any sense.

2. Apr 16, 2012