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

Calculate the probability density from the given wavefunction. $$|\Psi(x)|^2=A^2\sin^2 kx$$ a. The probability is highest where the probability density is maximum. A sine function’s maximum magnitude is 1. $\sin kx = \pm 1$ $kx=\frac{n \pi}{2}$, where n = 1, 3, 5,… $\frac{2 \pi x}{\lambda}=\frac{n \pi}{2}$, where n = 1, 3, 5,… $x=\frac{n \lambda}{4}$, where n = 1, 3, 5,… $x=\frac{ \lambda}{4}, \frac{3 \lambda}{4}, \frac{5 \lambda}{4}…$ b. The probability is zero where the probability density is zero. $\sin kx = 0$ $kx=n \pi$ where n = 0, 1, 2,… $\frac{2 \pi x}{\lambda}=n \pi$, where n = 0, 1, 2,… $x=\frac{n \lambda}{2}$, where n = 0, 1, 2,… $x=0, \frac{ \lambda}{2}, \lambda, \frac{3 \lambda}{2},…$