At time $t=0$ a particle is represented by a wave function given by \[ \psi(x, 0)=\left\{\begin{array}{ll} A(x / a), & (0 \leq x \leq a) \\ A(b-x) /(b-a), & (a \leq x \leq b) \\ 0, & \text { elsewhere } \end{array}\right. \] where $A, a$ and $b$ are positive constants. (a) Normalize the wave function $\psi$ (find $A$ in terms of $a$ and $b$ ). (b) Sketch $\psi(x, 0)$ as a function of $x$. (c) Where is the particle most likely to be found at $t=0$ ? (d) What is the probability of finding the particle in the region $x<a$ ? (e) Evaluate the expectation value of position, namely $\langle x\rangle$.

Public Answer

9BQ0HK The First Answerer