The energy shift of the transition in e.g. hydrogen arising from the interaction between vacuum energy fluctuations and the orbitals' electrons.
Questions tagged [lamb-shift]
28 questions
9
votes
3 answers
Lamb shift in hydrogen atoms
Has a Lamb shift been observed in any atom other than hydrogen?
I am highly confused. The Lamb shift makes the P1/2 state lower than the S1/2 state. Is Lamb shift observed in other atoms? If not, then why?
Shashank
- 101
8
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1 answer
Why does Lamb shift renormalization not affect decay rate?
As a preface, I know there are "more" correct ways to calculate the Lamb shift and decay rate through full blown QED, but this is what's most familiar with me, so I would appreciate an answer in this realm (without going to full QED and talking…
Electric to be
- 322
7
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0 answers
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 "interpretations": For example, one can say something like…
teemteem
- 71
5
votes
2 answers
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 \vec{r} \cdot…
lagrange103
- 457
4
votes
1 answer
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}$?
cover
- 189
3
votes
1 answer
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, is there any physical relationship between the Lamb…
connorp
- 401
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0 answers
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, and also the diagrams for emission of soft…
octonion
- 9,072
3
votes
2 answers
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 full QED treatment. I have seen Scully and Zubairy…
vivian
- 131
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0 answers
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$ coupled to the external electromagnetic field of…
Masterme
- 367
2
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1 answer
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 convinced as to why it doesn't affect all other…
user6760
- 13,214
2
votes
1 answer
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 can be created and destroyed, but we have to…
aitfel
- 3,123
2
votes
1 answer
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? What order in perturbation theory do you have to go up…
Dan
- 5,795
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1 answer
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 and shifts its energy level to that of the…
Thomas Wening
- 1,247
2
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0 answers
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 \rangle$, where $|i\rangle$ represents some…
Brian Bi
- 6,885
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0 answers
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},
$$
and the reduced Green's function as
$$G'_n(x,y,E_n)…
Veritas
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