Chapter 40, Problem 40.49P

(a)

To determine

The probability ${\left|\psi \right|}^{2}dx$ that the particle in a box in the first excited state will be found in the interval $x$ to $x+dx$ for $x=\frac{L}{4}$.

(b)

To determine

The probability ${\left|\psi \right|}^{2}dx$ that the particle in a box in the first excited state will be found in the interval $x$ to $x+dx$ for $x=\frac{L}{2}$.

(c)

To determine

The probability ${\left|\psi \right|}^{2}dx$ that the particle in a box in the first excited state will be found in the interval $x$ to $x+dx$ for $x=\frac{3L}{4}$.