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5
votes
0answers
147 views

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 "...
4
votes
2answers
89 views

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 ...
2
votes
0answers
83 views

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 ...
1
vote
1answer
853 views

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? ...
1
vote
1answer
68 views

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 ...
1
vote
0answers
41 views

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[...