2011-67.md

course	course_year	question_number	tags	title	year
Quantum Mechanics	IB	67	IB 2011 Quantum Mechanics	Paper 3, Section I, C	2011

A particle of mass $m$ and energy $E$, incident from $x=-\infty$, scatters off a delta function potential at $x=0$. The time independent Schrödinger equation is

$$-\frac{\hbar^{2}}{2 m} \frac{d^{2} \psi}{d x^{2}}+U \delta(x) \psi=E \psi$$

where $U$ is a positive constant. Find the reflection and transmission probabilities.