# Questions tagged [fermis-golden-rule]

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### How to prove that the spectral line-width is given by the imaginary part the self energy?

I am trying to understand the computational methods to calculate the spectral line-width as done in this paper, http://www.nature.com/articles/ncomms11755 Here, they say that the line-width is ...
24 views

### What is the difference between the joint density of states and the density of state?

I think I understood the density of states, but I didn't understand the joint DOS. What is the main difference? What is the exact definition of the joint DOS? When do we use the joint DOS and when do ...
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### Fourier transform of a scatering potential

The Fermi golden rules states $$\Gamma(\vec{k},\vec{k}') = \frac{2\pi}{\hbar} \left| \left \langle \vec{k}|V|\vec{k}' \right \rangle \right|^2 \delta(E(\vec{k})-E(\vec{k}')) \, .$$ Many places (for ...
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### How can a Dirac delta function that does not occur under an integral be used to describe a transition rate?

In his excellent notes (found here), Mark Tuckerman shows that the transition rate of absorption between quantum states i and f, coupled by operator B, can be expressed as the fourier transform of the ...
845 views

### What is the matrix element?

Can someone give me an Eli5 description of what the matrix element is, particularly in regards to Fermi's Golden Rule? Fermi's golden rule describes the likelihood of a transition per unit time. ...
193 views

### Probability density in Fermi golden rule

Consider Fermi golden rule $$\Gamma _{{i\rightarrow f}}={\frac {2\pi }{\hbar }}\left|\langle f|H'|i\rangle \right|^{{2}}\rho$$ I don't understand why $\left|\langle f|H'|i\rangle \right|^{{2}}$ is ...
111 views

### Fermi's golden rule (transition rate) for two widely separated states

My problem has to do with quantum (e.g. electronic) transitions of a single particle between two orthogonal states. I know, for example, that light can couple two orthogonal states in a Hydrogen atom ...
44 views

### Wigner-Ekhart theorem for Fermi Golden Rule in semiconductors

I have seen many authors mentioning that there is a way to work in total angular momentum basis and calculate the matrix elements using the Wigner-Ekhart theorem. Here the author even says that ...
63 views

### Why is it intuitively unreasonable for this transition probability to grow quadratically in $t$?

In Sakurai's "Modern Quantum Mechanics" section 5.6, there is a seemingly simple statement made that I do not understand the logic of. The author is considering a physical situation in which we "turn-...
78 views

### Identifying diagrams for optical processes

I was reading some papers on the study of the optical properties of some metals and came upon these conference proceedings by Hopfield from 1972. They are on the study of the infrared properties of ...
122 views

### What is norm of matrix element in Fermi Golden Rule

Fermi Golden Rule says: $\Gamma \propto |M_{ij}|^2$ I know how to get $M_{ij}$, but how do I proceed? How do I take a norm of Hermitian matrix? There is no clear (to me) definition in the internet ...
430 views

### Fermi Golden Rule derivation of quasi-electron lifetime

I wonder if there is a detailed derivation of the quasi-electron lifetime: \frac{1}{\tau_k}=\frac{2\pi}{\hbar}\frac{1}{V^2}\sum_{k', q}\sum_{\sigma}|V_q|^2f_{k'}(1-f_{k-q})(1-f_{k'+q}...
333 views

### How to explain the long lifetime of Rydberg atoms with Fermi golden rule?

How to explain the long lifetime of Rydberg atoms with Fermi golden rule? Wikipedia says it is partly due to tiny wavefunction overlap with inner orbitals, but what about the outer ones?