course | course_year | question_number | tags | title | year | |||
---|---|---|---|---|---|---|---|---|
Quantum Mechanics |
IB |
70 |
|
Paper 3, Section II, C |
2012 |
State the condition for a linear operator
Given the position and momentum operators $\hat{x}{i}$ and $\hat{p}{i}=-i \hbar \frac{\partial}{\partial x_{i}}$, define the angular momentum operators
$$\left[\hat{L}{i}, \hat{L}{j}\right]=i \hbar \epsilon_{i j k} \hat{L}_{k}$$
and use these relations to show that $\hat{L}{3}$ is Hermitian assuming $\hat{L}{1}$ and
Consider a wavefunction of the form
where