NAME:
Modern Physics: Quiz VI: Due before Midnight March
17, 2013: Only email answers accepted
(A) True or False, If false, correct it
(False)(1) At absolute zero, H-atom in a box will have zero energy.
(False)(2) Average momentum of a electron in a box is finite.
(True)(3) If the initial wave function is an eigenstate of the system, the probability density of the particle remains unchanged
with time.
(B)Short Questions
(1) If ψ(x) = ei3x , what is the average momentum of the particle
3h̄
(2) If ψ(x) = cos(2x), what is the average momentum of the
particle
Zero
(3) A free particle at t = 0 is described by ψ = A(sin(2x) +
3 cos(6x)). Write down the wave function at later time t. Here
A is a constant.
ψ(x, t) = A(sin(2x)eiE1 t/h̄ +3 cos(6t)eiE2 t/h̄ , where E1 = 4h̄2 /(2m)
and E2 = 36h̄2 /(2m).
(4) If ψ(x) = A[cos(2x) + sin(3x)], what is the average momentum of the particle.
Zero