A particle is in the ground state of an infinite square-well potential.The probability of finding the particle in the region 0

Question

A particle is in the ground state of an infinite square-well potential.The probability of finding the particle in the region 0 < x < L/3 is
A)0.41
B)0.25
C)0.20
D)0.34
E)0.27

Quizplus · Accepted Answer

The probability of finding the particle in a certain region is given by the integral of the squared wave function over that region. In this case, since the particle is in the ground state, its wave function is given by:

ψ(x) = sqrt(2/L) sin(pi*x/L)

The probability of finding the particle in the region 0 < x < L/3 is then:

P = integral[0 to L/3] |ψ(x)|^2 dx
  = integral[0 to L/3] (2/L) sin^2(pi*x/L) dx
  = (2/L) * (L/6 - sin(2pi/3)/(4pi))
  = 1/3 - (1/2pi)sin(2pi/3)
  ≈ 0.20

Therefore, the best choice is C.

A Particle Is in the Ground State of an Infinite