# Questions tagged [fermis-golden-rule]

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### How to deal with the appearance of delta functions in differential cross sections?

I've recently started learning quantum field theory, and I'm on chapter 3 of Hatfield's Quantum Field Theory of Point Particles and Strings. I was flipping through the book today, and I came across an ...
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1 vote
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### How does one use Fermi's Golden Rule to calculate two-body rate of collision for a 1-D Fermi gas?

I am trying to verify a simulation I made of a bunch of non-interacting fermions (except elastic collisions) in a harmonic potential by comparing the rate of collisions from my simulation by using a ...
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### Transitions in constant perturbations using time independent perturbation theory

The perturbed Hamiltonian is given as. $$H=\begin{cases} H^{(0)}&\text{for }t\leq 0 \\ H^{(0)}+V(x)&\text{for }t>0\end{cases}.$$ Here $V(x)$ does not depend explicitly on time but it can ...
• 261
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### Justification and interpretation of Fermi Golden Rule (second order) in Resonance Energy Transfer (RET)

I hope someone can give me some new insight to understand this. Fermi's golden rule is wildly used to calculate the rate for RET. I have some difficulties in understanding its justification and ...
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### Photoelectric effect in hydrogen: evaluating the matrix element integral

I'm following page 503 of Shankar's Principle of Quantum Mechanics. The author is discussing the photoelectric effect and transition from the hydrogen ground state to a plane wave. Applying the ...
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1 vote
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### Probabilities of transitions given by Fermi's golden rule

We were deriving Fermi's golden rule from first applying a weak time dependant (periodic) perturbation and then looking at first order changes to the Hamiltonian. We found that the probability of ...
• 1,357
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### Calculation of electromagnetic transition probability

I'm reading From Nucleons to Nucleus by Suhonen, where (page 118) he introduced the electric or magnetic (with an index $\sigma$ such that $\sigma = E$ or $\sigma = M$) by the formula, \begin{align} ...
• 59
231 views

### Fermi's Golden rule: Accounting for Decoherence

On the Wikipedia page for Fermi's golden rule, there is a vague statement that is given in passing: ... if there is some decoherence in the process, like relaxation or collision of the atoms, or like ...
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1 vote
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### Transition probability in the case of "strong" perturbation

We know that Fermi's Golden rule is true only for weak and short perturbation, when the transition probability $P_{fi}\ll 1$. But what if perturbation is relatively strong, so we can't use this ...
• 11
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### Limit of the $\sin^2$ function in the derivation of Fermi's golden rule

In the derivation of Fermi's golden rule one typically arrives at an expression of the form $$\frac{\sin^2(\omega t)}{\omega^2}$$ which is then converted to $$\pi t\delta(\omega).$$ I cannot ...
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1 vote
109 views

### Dirac delta function mathematical expression proof

In a discussion of the second order transitions in graphene this mathematical expression is used. $$\left|\frac{1}{\varepsilon + i \Gamma/2}\right|^2 = \frac{2\pi}{\Gamma}\delta(\epsilon)$$ And I'm ...
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1 vote
61 views

### 2 in the Fermi’s Golden Rule

In the derivation of the Fermi's golden rule many authors expand periodic perturbation in this form $$\hat{V}=\hat{F} e^{-i \omega t}+\hat G e^{i \omega t}$$ However I do not understand the reason. ...
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