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seen Jul 18 at 14:35

Jun
20
awarded  Yearling
Jan
24
awarded  Enthusiast
Jan
14
answered Why doesn't Newton's Second Law include higher-order mass?
Jan
14
comment Commutator of $L^2$ and $X^2$, $P^2$
I just went through the derivation of that identity, starting from (1) $U^{\dagger}\left(R\right) {\hat V}_i U\left(R\right) = R_{ij} {\hat V}_j$ with $U\left(R\right) = 1 - i \delta\theta \hat{\bf n} \cdot {\hat{\bf L}} / \hbar $ and $R_{i j} = \delta_{ij} + \delta\theta n_k \epsilon_{k j i}$. So I just need to think a bit more about where (1) comes from, and why this means $\hat{V}$ is a vector operator. I guess from the usual definition of a vector as something that transforms like a vector under rotations.
Jan
13
comment Commutator of $L^2$ and $X^2$, $P^2$
I don't want to derail this question, but I've never quite understood the last part of your answer about how an identity like $\left[X_i, L_j\right] = i \hbar \epsilon_{i j k} X_k$ means $X_k$ is a vector operator. Any good references or intuitive explanations for that?
Jan
13
revised Lorentz force equation from relativistic Lagrangian
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Jan
13
answered Lorentz force equation from relativistic Lagrangian
Jan
6
revised Aerodynamic drag on a cannonball?
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Jan
6
answered Aerodynamic drag on a cannonball?
Jan
6
answered Energy of electron accelerated by a magnet
Jan
5
revised Bound States clarification
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Jan
4
answered Bound States clarification
Jan
4
comment Energy and time evolution of a particle in a potential well
Gotcha, so it is a free particle after $t=0$. I updated my post to reflect this.
Jan
4
revised Energy and time evolution of a particle in a potential well
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Jan
4
comment Energy and time evolution of a particle in a potential well
I updated my answer again. Let me know if that doesn't make sense.
Jan
4
revised Energy and time evolution of a particle in a potential well
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Jan
4
revised Energy and time evolution of a particle in a potential well
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Jan
4
comment Calculate Hamiltonian from Lagrangian for electromagnetic field
Or, at least a power of $\partial_\mu A^\mu$.
Jan
4
awarded  Commentator
Jan
4
comment Energy and time evolution of a particle in a potential well
I made some more edits. The orthogonality condition allows you to pick out a single $c_n$ from the infinite sum.