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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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 ...
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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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General technique for solving non-scattering problems in quantum field theory

In quantum electrodynamics (QED), for example, we can calculate any scattering amplitude using the Feynman diagram perturbative expansion. That is, we can calculate the matrix element $\langle i | f \...
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What does $(\delta\vec{r}\cdot\nabla)^2$ mean in the derivation of the Lamb shift, and how do you find its expectation?

The Wikipedia page on the Lamb shift includes the following first steps: $$\Delta V = V\bigl(\vec{r}+\delta \vec{r}\bigr)-V(\vec{r})=\delta \vec{r} \cdot \nabla V (\vec{r}) + \frac{1}{2} \bigl(\delta ...
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Lamb shift and logarithmic corrections

Radiative corrections (Lamb shift) to the energy level (1S state) of a hydrogen atom can be written as a power series in $Z\alpha$ and $\ln(Z\alpha)$: $$\Delta E = \frac{\alpha}{\pi}(Z\alpha)^4 \left[...
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Relation between the reduced Green's function and the full Green's function

Let us assume that we have some Hamiltonian and we know its spectrum $$H_0 \psi_n = E_n \psi_n .$$ We define the Green's function in as $$ G(x,y,E) =\sum_m \frac{\psi_m^*(x)\psi_m(y)}{E-E_m}, $$ and ...
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Apparent Lamb Shift paradox

If the lamb shift causes the $^2$S$_{\frac{1}{2}}$ state to be higher in energy than $^2$P$_{\frac{1}{2}}$, why does the $^2$S$_{\frac{1}{2}}$? state not decay to $^2$P$_{\frac{1}{2}}$ Is there 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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How does one derive the Lamb shift for the Hydrogen atom?

I've been perusing my copies of Srednicki and Peskin & Schroeder, and I can't seem to find an explanation of how one derives the Lamb shift that I can follow. How does one derive the Lamb shift? ...