## University Physics with Modern Physics (14th Edition)

a. $x=0, L$ are the only solutions for x inside the box. b. $x=\frac{L}{2}$ is the only solution for x inside the box. c. Yes, this matches the picture.
Calculate the probability density from the given wavefunction. $$|\psi(x)|^2=\frac{2}{L}\sin^2 \frac{\pi x}{L}$$ a. The probability is zero where the probability density is zero. $\sin \frac{\pi x}{L}=0$ $\frac{\pi x}{L}=n \pi$, where n = 0, 1, 2,… $x=0, L$ are the only solutions for x inside the box. b. The probability is highest where the probability density is maximum. A sine function’s maximum magnitude is 1. $\sin \frac{\pi x}{L}=\pm 1$ $\frac{\pi x}{L}=\frac{n \pi}{2}$, where n = 1, 3, 5,… $x=\frac{L}{2}$ is the only solution for x inside the box. c. Yes, this matches the picture.