8. ### Adiabatic Approximation in Hydrogen Atom

Homework Statement Assume that Planck's constant is not actually constant, but is a slowly varying function of time, $$\hbar \rightarrow \hbar (t)$$ with $$\hbar (t) = \hbar_0 e^{- \lambda t}$$ Where ##\hbar_0## is the value of ##\hbar## at ##t = 0##. Consider the Hydrogen atom in this case...
9. ### I Probabilities Associated with Sudden Changes in Potential

Hi, I have a question about calculating probabilities in situations where a particle experiences a sudden change in potential, in the case where both potentials are time independent. For example, a tritium atom undergoing spontaneous beta decay, and turning into a Helium-3 ion. The orbital...
10. ### Finding the probability of 1s electron within a cubical volume

Homework Statement How to calculate the probability of finding an 1s electron within 1 picometer cubic region located 50pm from the nucleus. Homework Equations The probability of an 1s electron within a spherical volume of radius 'a' from nucleus can be find using the expression...
11. ### I Probability vs radial density-confusion

Hi everyone; A very stupid confusion here. When we want to talk about the most probable radius to find the electron in $1s$ orbital, why do we talk about the radial density and not the probability itself? For instance, the probability of finding the the electron at a radial distance $r$...
12. D

### Taylor expansion fine structure

I have to do a Taylor expansion of the energy levels of Dirac's equation with a coulombian potential in orders of (αZ/n)^2 , but the derivatives I get are just too large, I guess there is another approach maybe? This is the expression of the energy levels And i know it has to end like this:
13. ### Normalizing the wave function of the electron in hydrogen

Homework Statement I am having trouble with part d, where they ask me to prove that the wave function is already normalized The Attempt at a Solution But that clearly doesn't give me 1. I tried to use spherical coordinates since it is in 3D? Not really sure how to proceed. EDIT: I realize...

24. ### Binding energy og H-1

Hello Friends !! I have a question regarding binding energy... Trying to calculate the binding energy of H-1 (hydrogen nucleus). Well it is obvious that the binding energy is zero since there is no other nucleons that the proton is bound to. But after having collected the best possible data of...
25. ### Hydrogen atom in mixed state

Suppose a single hydrogen atom is in mixed state. Ψ=(1/√2) Ψ_100+(1/√2) Ψ_200 Then energy will be E=(1/2)*13.6+(1/2)*(3.4)=8.5 eV. But there is no spectral line at 8.5 eV.
26. ### Hydrogen atom ground state wave function complex conjugate

For hydrogen atom ground state we know φ=π-1/2a-3/2e-r/1 I want to know the complex conjugate of φ* ?
27. ### Hyperfine structure in hydrogen

Consider the Dirac equation for bounded electron in hydrogen atom. I am trying to get a clear physical explanation for all mathematical terms that appear in the Hamiltonian and energy spectrum. Kinetic and Coulombic potential and rest energies are the first terms and easy to identify. Then we...
28. ### Dimensionless Radial Equation Hydrogen Atom

Homework Statement Show that in terms of the dimensionless variable ##\xi## the radial equation becomes ##\frac{\mathrm{d}^{2} u}{\mathrm{d} \xi^{2}}=(\frac{l(l+1)}{\xi^{2}}-\frac{2}{\xi}-K)u## Homework Equations ##u(r)\equiv rR(r)## ##\xi \equiv \sqrt{2\mu U_{0}}\frac{r}{\hbar}##...
29. ### Ionization of hydrogen atom by sinusoidal electric field

Homework Statement "Suppose that a hydrogen atom, initially in its ground state, is placed in an oscillating electric field ##\mathcal{E}_0 \cos(\omega t) \mathbf{\hat{z}}##, with ##\hbar \omega \gg -13.6\text{eV}##. Calculate the rate of transitions to the continuum." Homework Equations ##R =...
30. ### Difference of Hydrogen Hamiltonian with relative mass particles

Hi guys, I consider the qm-derivation of the electronic states of hydrogen. There are two different derivations (I consider only the coulomb-force): 1) the proton is very heavy, so one can neglect the movement 2) the proton moves a little bit, so one uses the relative mass ##\mu## The...