A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at t=0.
The Attempt at a Solution
I know the process of solving PDE's clear as day, thats not the issue. The problem is that I'm tripping myself out on how to write Ψ(x,t) as a linear combination of its ground state + first excited state.
My hunch is to approach the problem like this :
where 1 and 2 represent the ground state and first state, respectively
that momentum takes on the largest possible value at t=0 is confusing and not sure what to do.