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 E 1 2 2 2mL 2 (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 E 1 What is the probability that the particle is in the left half of the box VI 3 1 (x) V2 342(x)

Question: A quantum particle is restricted to a one dimensional box 0 ? x ? L. It experiences no forces within the box, but cannot escape.

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

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

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?

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

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