Quantum Mechanics - Probability

The wave function for a particle constrained to move in one dimension is shown in the graph (Ψ = 0 for x ≤  0 and x ≥ 5). What is the probability that the particle would be found between x = 2 and x = 4?

A. 17/64
B. 25/64
C. 5/8
D. v(5/8)
E. 13/16

(GR9677 #17)

Solution:

Probability, P ∼ ψ²

Probability to find the particle between x = 2 and x = 4 (unnormalized probability):
ψ² = 2²  + 3² = 13

Total probability (normalized probability):
ψ² = 1²  +  1²  + 2²  + 3²  +  1² = 16

P = unnormalized probability / normalized probability = 13/16

Answer: E