(a) Compute < x > and σ^2 (b) Calculate the momentum probability density.

Question

The state of a free particle is described by the following wave function (Fig. 3.1) 

ψ(x) = 0 for x < −3a 

= c for − 3a < x < a 

= 0 for x > a

(a) Compute < x > and σ² 

(b) Calculate the momentum probability density.

Answer 1

 (a) The expectation values are

(b) Momentum probability density is |ϕ(p)|²