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What is the difference between Fermi golden rule and Wigner-Weisskopf theory?

What is the difference between Fermi golden rule and Wigner-Weisskopf theory? They both deal with the spontaneous emission process. So what is the difference? As far as I know, the fermi golden rule ...
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45 views

Physical meaning of the coupling matrix in Fermi golden rule

I am calculating the energy transfer rate using Fermi golden rule where the coupling matrix $M$ is obtained using second order pertubation method. $$ \Gamma_{tran}=\frac{2\pi}{\hslash}|M|^{2}\rho$$ ...
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1answer
44 views

What is the sum over the transition rates?

I was looking at the solution to an exercise, and I came over this expression: $$P_{i\to f} = \sum \limits_{f} {2 \pi \over \hbar }\; |\langle f |\hat V | i \rangle |^2 \delta(E_{fi}-E),$$ where ...
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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 ...
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3answers
278 views

Simple real-life examples of Fermi's golden rule?

I want to teach my students some simple applications of Fermi's Golden Rule. Unfortunately, most examples I can think of are in scattering theory, which they have not learned yet. Are there any ...
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37 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?
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126 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 ...
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96 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 ...
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1answer
145 views

Why doesn't Fermi's golden rule distinguish attraction from repulsion?

Let's say I have two distinguishable charged particles interacting electrostatically. In Fermi's golden rule, the two particles can change state at a rate proportional to: $$|\langle \psi_f | H_{int} ...
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39 views

Physical interpretation of Fermi golden rule? [duplicate]

What is the physical interpretation of Fermi's golden rule?
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0answers
57 views

What is the physical meaning of the “decay rate” in Fermis golden rule? [duplicate]

As far as I understood, Fermi's golden rule gives a prediction of the transition rate in a perturbed quantum system $H_0+V$ between two eigenstates of the unperturbed system $H_0$, say from $\left| ...
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0answers
112 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, ...
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3answers
2k views

Interpretation of “transition rate” in Fermi's golden rule

This is a question I asked myself a couple of years back, and which a student recently reminded me of. My off-the-cuff answer is wrong, and whilst I can make some hand-waving responses I'd like a ...
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1answer
125 views

Why multiply by volume when integrating over final momenta in scattering amplitude calculations?

I am learning about calculating decay rates from quantum field theory amplitudes from David Tong's lecture notes (page 74 in the notes, 24 in document). However, I have some doubts: When he says the ...
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1answer
317 views

Fermi's golden rule and Probabilities in QM

In Fermi's golden rule $$P_{ab}(t)=2\pi t/\hbar \left|\langle\psi_b|V|\psi_a\rangle\right|^2 \delta(E_f-E_i)$$ for transition probability from state $a$ to $b$, how can the probability grow with ...
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1answer
288 views

Density of States for Fermi's Golden Rule

I recently read a question on fermi's golden rule posted here: Fermi's Golden Rule and Density of States However, I do not really know how you would go about obtaining a value for the density of ...
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3answers
2k views

Fermi's Golden Rule and Density of States

I know Fermi's Golden Rule in the form $$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$ where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition ...
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269 views

Irreversibility and the Fermi golden rule

When a quantum system is perturbatively coupled to a continuum of states, one uses the Fermi's golden rule to compute the rate of transition form an initial state to a set of states contained in an ...
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1answer
1k views

Cross-section in relativistic limit: Fermi's golden rule still valid?

In order to calculate the cross-section of an interaction process the following formula is often used for first approximations: $$ \sigma = \frac {2\pi} {\hbar\,v_i} \left| ...
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1answer
535 views

Universality in Weak Interactions

I'm currently preparing for an examination of course in introductory (experimental) particle physics. One topic that we covered and that I'm currently revising is the universality in weak ...
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1answer
851 views

What is the range of validity of Fermi's Golden Rule?

It is well known that to calculate the probability of transition in the scattering processes, as a first approximation, we use the Fermi golden rule. This rule is obtained considering the initial ...