Question

For the wavefunction Ψ(x,0)= 1/√a for –a ≤ x ≤ a, find the momentum space wavefunction φ(k) A particle of mass m is trapped in a one dimensional box of width a. The wavefunction is known to be: Ψ(x) = (i/2)(√(2/a))Sin(πx/a) + (√(1/a))Sin(3πx/a) -1/2(√(2/a))Sin(4πx/a)

(a) If the energy is measured, what are the possible results and what is the probability of obtaining each result.

Answer 1

Answer

a)

Wavefunction tells the actual representation of particle's position.

b) To calculate the probability of an eigenvalue of an observable being measured, you must calculate the probability

P(t)=⟨λ∣Ψ(t)⟩⟨Ψ(t)∣λ⟩

for each eigenvector of the eigenvalue. For non-degenerate states, there will be one and this will be the probability.