Chapter 41, Problem 41.43P

(a)

To determine

The probability that the particle in the three-dimensional box in the ground state will be found somewhere between $x=0$ and $x=\frac{L}{2}$.

(b)

To determine

The probability that the particle in the three-dimensional box in the ground state will be found somewhere between $x=\frac{L}{4}$ and $x=\frac{L}{2}$ and to compare the results with the probability of finding the particle in the region $x=0$ to $x=\frac{L}{4}$ in example 41.1.