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Results tagged with homework-and-exercises
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user 29792
Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.
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Angular Momentum commuting with Hamiltonian
I've been given an assignment where I have to prove that the angular momentum operators $L_j = \varepsilon_{jkl}q_{k}p_{l}$ commute with the Hamiltonian, given as $H = \frac{p^2}{2m} + V(r)$.
Now, I …
- 205
0
votes
0
answers
778
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Quantum Hamiltonian commuting with the Pauli-Runge vector
I have to prove that $[A_j, H] = 0$, with;
$$\vec{A} = \frac{1}{2Ze^{2}m}(\vec{L} \times \vec{P} - \vec{p} \times \vec{L}) + \frac{\vec{r}}{r}$$
$$H = \frac{p^2}{2m} - \frac{Ze^2}{r}$$
And, $Z, e, m …
- 205
1
vote
1
answer
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Commutation of abstract $O(3)$ generators and vectors [closed]
I've been given the following problem, and I'm quite lost with it.
Let $L_1$, $L_2$, and $L_3$ denote the abstract $o(3)$ algebras. You are given that $\vec{A} = (A_1, A_2, A_3)$ and $\vec{B} = (B_1, …
- 205
3
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0
answers
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Fock Subspaces and Weight Vectors
This is my first time taking a physics course (I'm a mathematics major), so I'm encountering a lot of new things, which I'm kind of expected to know. In particular, how to work with Bosons.
I've got …
- 205