A quantum particle is restricted to a one dimensional box 0 ? x ? L. It experiences no forces within the box, but cannot escape. At time t = 0, the particle is in the state

?

where ?_i(x) are the (correctly normalized) energy basis states from eq.?

(a) Compute the probability at t = 0 that the particle has energy ? = E₁ = ?²?²/2mL².?

(b) Compute the probability at t = 0 that the particle is in the left half of the box (x

(c) Compute the state of the particle at time t = ??/?. What is the probability at this time that the particle has energy ? = E₁? What is the probability that the particle is in the left half of the box?

Transcribed Image Text:

VI/3 1 (x) + V2/342(x)