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4
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0answers
166 views

Delta normalization and density of states in the Golden rule of Fermi

In the text-book derivation of first order inelastic scattering amplitude, box normalization is usually used to calculate the result. This leads to a correct result through the Golden Rule of Fermi, ...
3
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0answers
87 views

Gauge invariance of Fermi's golden rule

I am having some issues with gauge invariance of Fermi's golden rule. Say we have a system Hamiltonian for a particle in an electric field and some additional potential $V$ with \begin{equation}H=(p-A(...
1
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0answers
28 views

Normalize plane wave on an infinite domain.

I need to make an exercise related to quantum mechanics. (Specifically I need to apply Fermi's golden rule where the initial and final states are both plane waves). The system is 1 dimensional, ...
1
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0answers
22 views

How to calculate the resonance peak of a NV center during a ESR/ODMR measurement?

I am thinking of making an magnetometer with ODMR measurement of a NV center in nanodiamond. But before I do the experiment, I want to estimate the sensitivity of my experiment beforehand ...
1
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0answers
43 views

Fermi Golden Rule derivation of quasi-electron lifetime

I wonder if there is a detailed derivation of the quasi-electron lifetime: \begin{equation} \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}...
1
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0answers
377 views

Why doesn't Graphene have a band gap?

Is there any simple justification about graphene having no band gap? How bout its linear E-K? Why bilayer graphene has a quadratic E-K and electric field can open a band gap there? I do not ...
1
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0answers
119 views

When is Fermi golden rule exact?

My recent study Nonsmooth and level-resolved dynamics illustrated with a periodically driven tight binding model motivates me to ask this question: Is there any example in which the Fermi golden rule ...
0
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0answers
32 views

Fermi's golden rule and the DoS of scattering states

Can the Fermi's golden rule $$\Gamma_{fi} ~=~ \rho(E_f) \frac{2\pi}{\hbar} |M_{fi}|^2$$ be applied for transitions of discrete states to scattering states? If yes, then what should the density of ...
0
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0answers
52 views

Is the Fermi golden rule really accurate for calculating the life time of an atomic level?

In my impression, Fermi golden rule is routinely used in calculating the life time of an excited atomic level. But it is based on the first order perturbation theory, so it is not expected to be ...
0
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0answers
29 views

Quasi-electron lifetime at Dirac (Weyl) point

I would like to know how one should calculate the electron lifetime with chemical potential at the Dirac point from Fermi Golden Rule: \begin{equation} \frac{1}{\tau_k}=\frac{2\pi}{\hbar}\frac{1}{V^2}...
0
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0answers
17 views

One dimensional decay biggest contribution

I have a one-dimensional system of interacting particles. If I now want to calculate the decay rate of a one-particle initial state, I was told that the biggest contribution to the decay comes from ...
0
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0answers
28 views

Evaluation of a probability from Fermi Golden rule

In Marc Bee's book, he has described the principle of spectroscopy with reservoir (the material) and the probe as interacting systems with their own hamiltonians $H_R$ and $H_p$ respectively and $H_c$ ...
0
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0answers
86 views

Relativistic Fermi Golden Rule?

On online slide notes, it is mentioned that: Fermi Golden Rule: $$P_{if}=\frac{2\pi}{\hbar}|M_{if}|^2\rho_f$$ where $\rho_f$ is density of final sates --number of quantum states per unit volume - ...
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0answers
47 views

Can the half-life of rubidium 87 be theoretically estimated?

Can the Fermi golden rule be applied to give an approximation of this half-life?