# Tagged Questions

1answer
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### Finding the wavelength of an electron in its ground state?

To find the wavelength of an electron in its ground state in a hydrogen atom, would I or could I do the following? Use the ground state energy (-13.6eV) in $E^2 = m^2c^4 + p^2c^2$ Solve for $p$ Use ...
2answers
174 views

### Technical detail in the solution of the hydrogen atom

I'm trying to do an exercise in which you solve the Schrödinger equation for the hydrogen atom. Through the exercise, I've already shown that the wavefunction is:  \psi_{n\ell m}(r,\theta,\varphi) ...
2answers
468 views

### Wave function of Hydrogen Atom

Wavefunction of a Hydrogen atom is expressed in eigenfunctions as: $$\psi(\boldsymbol r,t=0)=1/\sqrt{14}(2\psi_{100}(\boldsymbol r)-3\psi_{200}(\boldsymbol r)+\psi_{322}(\boldsymbol r) ).$$ Is ...
1answer
180 views

### Electric dipole transitions/expectation value of position

Part of a homework question asks to show that for $\ell=0$ in both $\Psi_i$ and $\Psi_f$, we have $$\int \Psi_i^\ast \vec{r} \Psi_f \; d\tau = 0$$ for the position vector $\vec{r}$. (This is for ...
0answers
300 views

### Square of Laplace–Runge–Lenz vector in Hydrogen atom [closed]

I have a problem. I've tried this question, but I don't get the correct expression. Can someone give me some ideas? Thanks! Consider the Hydrogen Atom Hamiltonian:  H = (\mathbf p^2/2 ...
0answers
307 views

### Evaluating Transition probability between different states of Hydrogen atom

I am trying to evaluate the inner product $<2S_{\frac{1}{2}},F',F'_{3}|\delta^{3}(x)\sigma_{i}P_{i}|2P_{\frac{1}{2}},F,F_{3}>$ It's written in the form $<nl_{j},F,F_{3}|$ Where ...
1answer
376 views

### Plotting Hydrogen's $2P_{x,y,z}$ Probability Densities in MATLAB [closed]

I have spent an unreasonable amount of time trying to plot $F(r,\theta,\phi)$ plane slices in MATLAB. I want to look at $x-y,y-z,x-z$ planes. Here's the function, specifically: ...
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