2017-67.md

course	course_year	question_number	tags	title	year
Quantum Mechanics	IB	67	IB 2017 Quantum Mechanics	Paper 4, Section I, B	2017

(a) Give a physical interpretation of the wavefunction $\phi(x, t)=A e^{i k x} e^{-i E t / \hbar}$ (where $A, k$ and $E$ are real constants).

(b) A particle of mass $m$ and energy $E>0$ is incident from the left on the potential step

$$V(x)=\left{\begin{array}{cl} 0 & \text { for }-\infty<x<a \\ V_{0} & \text { for } a<x<\infty \end{array}\right.$$

with $V_{0}&gt;0$.

State the conditions satisfied by a stationary state at the point $x=a$.

Compute the probability that the particle is reflected as a function of $E$, and compare your result with the classical case.