Recent content by Danielk010

Sorry, I tried to insert LaTeX in the TL;DR but it did not display correctly. I am also past the time limit to edit a post. Here is the problem: The spin Hamiltonian for a spin-1/2 particle in an external magnetic field is $$\hat{H} = -\hat{\mu} * B = - \frac{gq}{2mc}\hat{S} * B$$ Take ##B =...

I understand that the first order results would be ##\langle \phi_n^0 | -\mu * B | \phi_n^0 \rangle## = ##\langle \phi_n^0 | -\frac{gq}{2mc}\hat{S} * B | \phi_n^0 \rangle##, the second order results would be ##\sum_{k \ne n} \frac{|\langle \phi_n^0 | -\mu * B | \phi_n^0 \rangle|^2} {E_n^{(0)} -...

Hi, thank you response. This is from an homework problem, in which the TA for my class has already provided us the solution. They don't explain how: $$xe^{\frac{-ipx}{\hbar}} = i\hbar \frac{d}{dp} e^{\frac{-ipx}{\hbar}}$$ If I insert the completion relation of the eigenbasis of x (assuming this...

The equation comes from the solution of a homework equation we were given from A Modern Approach to Quantum Mechanics: 2nd edition by Townsend: $$ \textbf{Show} \langle p | \hat{x} | \psi \rangle = i \hbar \frac{\partial}{\partial p} \langle p | \psi \rangle $$ and $$ \langle \varphi |...

I do understand how to apply the product rule for differentiation and take the derivative of the exponential function. Thank you so much for the help. I got the answer.

From the rightmost part of the equation, $$\int dx \, \psi^*(x) \frac{\hbar}{i} \frac{\partial}{\partial x} \psi(x) (e^{{-i p_0 x / \hbar} + {i p_0 x / \hbar}})$$ which should make ## \langle p \rangle ## = ## \langle p \rangle ##, not ## \langle p \rangle ## = ## \langle p \rangle + p_0 ##...

I am stuck on proving: ##\langle p_x \rangle \rightarrow \langle p_x \rangle + p_0## given ##\langle x \mid \psi \rangle \;\rightarrow\; e^{i p_0 x / \hbar}\,\langle x \mid \psi \rangle## I was able to prove given the change in wave function mentioned above: ##\langle x \rangle \rightarrow\...

I first approached this problem with the idea that I could try to find the temperature of the HII region given that we already know the background temperature. Still, I am stuck on finding the region's temperature. A second approach was to try to find if the cloud is optically thick, which...

I got it. Thank you so much for the help

The continuity for the first derivative of which wave function?

From my understanding, you can equate ψ1(x) and ψ2(x) at the boundary of x = a, so I plugged in the values of a into x for both equations and I got ψ1(x) = 0 and ψ2(x) = ## (a-d)^2-c ##. I am a bit stuck on where to go from here.

oohhh. I got it. thank you for the help

Oh my bad. All of the values in Bohr's radius are constants if I am not mistaken. ##a_0 = \frac {4\pi\varepsilon_0\hbar^2} {m_e*e}##. 4, \pi, \hbar and the permittivity are all constants. An electron's rest mass is constant (##0.511 Mev##), and the elementary charge of an electron is also a...

all of the values except m

Solve for r, and then plug it in? ## r = \frac {C_1} {E-C_2} ##