# Tagged Questions

13 views

If $A$ and $B$ are Hermitian operators, show that $$C~:=~i[A,B]$$ is Hermitian too. My work: $$\begin{gather} C=i(AB-BA) \\ \langle\psi\rvert C\lvert\phi\rangle = i\langle\psi\rvert ... 1answer 28 views ### calculating degenerancy Given a function of two positive integers n_x^2+n_y^2. n_x^2+n_y^2=50 has three combinations of n_x and n_y that result in n_x^2+n_y^2=50:$$n_x=7,n_y=1n_x=5,n_y=5n_x=1,n_y=7$$... 0answers 35 views ### Fock Subspaces and Weight Vectors I've got an assignment due in a few hours, and I'm at a complete loss as to how to even start it, really. I haven't encountered any Dirac notation before, so I'm having a lot of trouble attempting the ... 1answer 68 views ### Quantum Hamiltonian commuting with the Pauli-Runge vector. I have to prove that [A_j, H] = 0, with;$$\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}$$And, Z, e, ... 0answers 22 views ### Commutation with a Hamiltonian analogue I've been given the problem of showing the following commutation;$$[A_{j} , H] = 0With H = \frac{p^2}{2m} - \frac{Ze^2}{r}. Now, I'm assuming that the A_j are Runge vectors (but, they might ... 1answer 67 views ### Calculate spin wave function given probabilities of its alignment along 2 axes Problem: An e^{-} exists in such a state that the probability of its spin aligning across the x_{(+)} axis is P_{x+}=1/2 and across the y_{(+)} axis is P_{y+}=1/2 as well. What is the spin ... 1answer 55 views ### 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 ... 0answers 34 views ### Statement about density operators, proof feedback I'm trying to solve the following exercise: Let V,W be finite dimensional inner product spaces over \mathbb{C}. Show that for every \psi \in V\otimes W with \langle \psi, \psi ... 5answers 110 views ### General solution of \frac{d^{2}u}{d\rho^{2}}=\frac{l\left(l+1\right)}{\rho^{2}}u In his discussion of the radial wave function of hydrogen Griffiths (Introduction to Quantum Mechanics, 2nd ed, p.146) gives the general solution ... 2answers 193 views ### Instance of Ehrenfest's Theorem Please Help me to fill in the gaps Show \frac{\text d \langle {p} \rangle}{ \text{d} t} =\left\langle - \frac{ \partial V }{\partial x} \right\rangle .\frac{\text d \langle {p} ...
Let $\rho_{AB}$ be the state of a composite quantum system with state space $H_A\otimes H_B$ (two finite dimensional Hilbert spaces). Now assume that $A$ and $B$ are isolated and suffer a unitary ...