Tagged Questions
1
vote
1answer
83 views
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 ...
4
votes
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:
$$ \psi_{n\ell m}(r,\theta,\varphi) ...
1
vote
2answers
468 views
Wave function of Hydrogen Atom
Wavefunction of a Hydrogen atom is expressed in eigenfunctions as:
$$\psi(\boldsymbol r,t=0)=1/\sqrt{14}(2\psi_{100}(\boldsymbol r)-3\psi_{200}(\boldsymbol r)+\psi_{322}(\boldsymbol r) ).$$
Is ...
2
votes
1answer
180 views
Electric dipole transitions/expectation value of position
Part of a homework question asks to show that for $\ell=0$ in both $\Psi_i$ and $\Psi_f$, we have
$$
\int \Psi_i^\ast \vec{r} \Psi_f \; d\tau = 0
$$
for the position vector $\vec{r}$. (This is for ...
1
vote
0answers
300 views
Square of Laplace–Runge–Lenz vector in Hydrogen atom [closed]
I have a problem. I've tried this question, but I don't get the correct expression. Can someone give me some ideas? Thanks!
Consider the Hydrogen Atom Hamiltonian:
$$
H = (\mathbf p^2/2 ...
0
votes
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 ...
0
votes
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:
...
