6) A particle in the infinite square well has the initial wave function
Ψ(x,0)= Ax when 0<=x<=a/2
Ψ(x,0)= A(a-x) when a/2<=x<=a
a) Sketch Ψ(x,0), and determine the constant A.
b) Find Ψ(x,t)
c) Compute <x> and <p> as functions of time. Do they oscillate? With what frequency?
Schrodinger Equation, Equations for expectation values
The Attempt at a Solution
Part (a) wasn't a problem. I solved for the normalization constant A by setting the integral of the norm of the wave function equal to zero.
A = 2 * sqrt(3/a^3)
Part (b) also wasn't a problem as Ψ(x,t)=Ψ(x,0)exp(-iEt/h)
Part (c) confuses me a little. I know how to calculate <x> and <p> using the equations <x> = ∫ψ*(x)xψ(x)dx and <p> = ∫ψ*(x)(h/i)d/dx(ψ(x))dx. But the as functions of time confuses me. Won't the exp(-iEt/h) cancel out when multiplied by its conjugate. If this is true, then how can <x> and <p> oscillate? How could they oscillate with any frequency? Any help would be appreciated.