# Questions tagged [lamb-shift]

The energy shift of the transition in e.g. hydrogen arising from the interaction between vacuum energy fluctuations and the orbitals' electrons.

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### Definition of internal energy for quantum systems

In the last days I questioned my self on the definition of internal energy in quantum systems. Let consider a bipartite system with hamiltonian $H^{AB} = H^A + H^B + V^{AB}$ for instance. Then, if the ...
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### Inconsistency between the Lamb shift and vacuum polarization

According to Griffiths' Introduction to Elementary Particles, one of the contributions to the Lamb shift is the lack of vacuum polarization. In chapter 2, he explains how vacuum polarization can be ...
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### Does the Lamb shift occur only in $n=2$?

Could the Lamb shift be used in $n=3,4,5,...$? Or does it only work with $n=2$? And does it work for values of $j$ other than $\frac{1}{2}$?
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### The most precise analytic solution of the hydrogen energy levels [closed]

Consider the problem where we want to calculate the energy levels of an electron in a hydrogen atom and we want to find the most precise analytic (i.e. a closed-form solution) solution that matches ...
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### Do $2s$ and $2p$ orbitals have same energy?

While solving the Schrodinger equation for the H atom, we get $E_n$ depending exclusively on $n$ (actually on $\frac{1}{n^2}$). Then I thought 2s and 2p orbitals must have the same energy. But while ... 119 views

### Question on lamb-shift calculation in Weinberg's QFT book

In short, how does one reproduce the derivation in the footnote on page 588 of Weinberg's QFT book? The derivation there are necessary for lamb-shift calculation. Complete version of my question: ...
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### Why does the $2p$ orbital have lower energy than $2s$? [duplicate]

I know there already are questions about this. But I find some error there. So, I asked again.... The answers I have read mostly point out that electrons in 2s orbital have a higher probability to be ...
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### Position measurement and hydrogen atom in QFT

I tried to give a QFT description of the hydrogen atom (at least conceptually and without going into mathematical details). The system is made by a spin$\frac{1}{2}$ fermion (electron) field $\phi_s$ ...
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### Do QED effects make a huge change to the position of the electrons?

In https://en.wikipedia.org/wiki/Lamb_shift about the lamb shift, it's mentioned that the change in the electron's frequency due to QED effects (vacuum polarization and self-energy correction) is ...
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### What parameters determine the amount of Uehling potential and self-energy correction effects?

Uehling potential correction and electron self-energy correction are the two most important factors contributing to the lamb shift in the hydrogen atom, by "smearing" the wavefunction of the electron. ...
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### If lamb shift is really due to the effect caused by virtual particles how come it only affect 1 orbital?

I was watching a video explaining virtual particle can be drawn to the positively charged necleus which explain why there is a tiny step between the higher energy level and ground state, but I'm not ...
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### Lamb Shift and virtual particles [closed]

Can someone explain about the Lamb Shift?
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### Why is the energy of $2s_{1/2}$ greater than the energy of $2p_{1/2}$ after the Lamb shift is taken into account?

The Wikepedia article here defines Lamb shift as a difference in energy between two energy levels $2s_{1/2}$ and $2p_{1/2}$ (in term symbol notation) of the hydrogen atom which was not predicted by ...
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### Second-order perturbation and photon creation

During the calculation to compute the shift of the energy of the hydrogen atom due to the photons by perturbation theory Schwartz states that At second order in perturbation theory, only one photon ...
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### Resonant frequency shift for cavity superconducting circuits

For superconducting circuits coupled to a resonator, we get a shift in the transmission spectrum (vacuum Rabi splitting) because of the interaction of the qubit and the resonator. Then one goes to ...
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### What is the difference between Lamb shift and the Darwin term?

I am currently learning for an exam and I wonder what the difference between the Lamb shift and the Darwin term is. What I know is that the Darwin term affects only the s-states of the hydrogen atom ...
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### Why does the Lamb shift only affect s-states?

The shift is due to interactions between atomic electrons and vacuum state fluctuations, so I would think that there would be an associated energy shift for all states, and not just s-states. Also, ...
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### Infrared divergence in scattering via annihilation

In textbooks when discussing radiative corrections to QED scattering they normally only consider the loops corresponding to the vertex function and corrections to the electron and photon propagators, ...
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### Hydrogen in an electromagnetic field bound states for full quantum electrodynamics

I am looking for a reference or derivation of the non-relativistic bound states of hydrogen in an electromagnetic field that include Zeeman effect, Stark shift, and Lamb shift. I am looking for a ...
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### Is it reasonable to interpret the Lamb shift as vacuum induced Stark shifts?

This is a pretty hand-wavy question about interpretation of the Lamb shift. I understand that one can calculate the Lamb shift diagrammatically to get an accurate result, but there exist "...
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