Question

For the infinite square-well potential, find the probability that a particle in its fourth excited state is in each third of the one-dimensional box:

a)  (0 ≤ x ≤ L/3)

b) (L/3 ≤ x ≤ 2L/3)

c) (2L/3 ≤ x ≤ L)

Answer 1

The wave function of the particle in fourth excited state (n = 5) is

The probability density is square of wave function

The integration of the of the probability density gives

a) Therefore probability for the particle to be from x = 0 to x = L/3 is

b) probability for the particle to be from x = L/3 to x = 2L/3 is

c) probability for the particle to be from x = 2L/3 to x = L is