Questions tagged [fermis-golden-rule]
141 questions
46
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5 answers
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 canonical one!
In the derivation of Fermi's Golden…
not all wrong
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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:
$$
\sigma = \frac {2\pi} {\hbar\,v_i} \left| M_{fi}\right|^2\varrho\left(E_f\right)\,V
$$
$$
M_{fi} =…
Chris
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Transition probability derivation: How to prove $\lim_{\alpha\rightarrow\infty} \frac{\sin^2\alpha x}{\alpha x^2} ~=~\pi\delta(x)$?
How to prove
$$\lim_{\alpha\rightarrow\infty} \frac{\sin^2\alpha x}{\alpha x^2} ~=~\pi\delta(x)~?$$
I have encountered this limit while learning time dependent perturbation and transition probability in Sakurai. How to show this limit? I tried to…
levitt
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Energy conservation for finite times in Fermi’s Golden Rule
In the derivation of Fermi’s Golden rule for the application of a sudden constant perturbation, we get the following formula for the rate:
$$ P_{f \leftarrow i}(t) = |\langle f|V|i\rangle|^2 \frac{4\sin^2\left(\frac{\omega_{fi}t}{2}\right)}{(E_f -…
Alex Gower
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Naive question about time-dependent perturbation theory
In time-dependent perturbation theory where $H=H_0+V$ and $V$ is considered small and has no explicit time dependence, the standard text-book treatment of the leading order probability amplitude for the system to make a transition from $|i\rangle$…
QuantumDot
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Fermi's golden rule and S-matrix
As I understand, Fermi's golden rule is a result from first order perturbation, which says that the transition rate of an initial state $|i\rangle$ to a final state $|f\rangle$ is
$$
\Gamma_{i\rightarrow f} =2\pi \rho|\langle f |H'|…
Daps
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Why is Schrödinger's cat in a superposition and not a mixture if you model decay with Fermi's golden rule?
I am teaching quantum information for undergraduate math students and as a perspective I thought it would be cool for them to discuss Schrödinger's cat a bit.
More precisely I'd like to come up with some explaination of how the cat gets to the…
11
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1 answer
Arbitrary normalisation of a free particle wave function
$\newcommand{\vec}[1]{\mathbf{#1}}
\newcommand{\dd}{\mathrm{d}}$I'm reading Landau and Lifshitz' book on non-relativistic quantum mechanics and I have some doubts about a passage in the chapter about elastic scattering. I have the French edition of…
yellon
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Universality in Weak Interactions
I'm currently preparing for an examination of course in introductory (experimental) particle physics. One topic that we covered and that I'm currently revising is the universality in weak interactions.
However I don't really understand the point my…
fermi333
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Fermi's golden rule and infinite probablity?
I am slightly confused about the application of Fermi's golden rule. Which during standard derivations indicates a probability of transitioning from the state $|i \rangle$ to the state $|f\rangle$ of:
$$P=\frac{2\pi t}{\hbar^2} | \langle f | \hat V…
8
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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 matrix elements.
I'm struggling to do a derivation…
Edward Hughes
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What is the Quantum Transition Time for Photon Emission?
When an electron in an atom changes energy states to emit a photon, how long does the process take? Is this question even meaningful?
user56903
7
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1 answer
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 noise in the perturbation, in which case the…
Sahand Tabatabaei
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Is there any simple way to predict beta decay half lives?
Question
For nuclides that decay by alpha emission, the Geiger-Nuttall law gives a simple and reasonably accurate estimate of the half-life. Essentially, one can model the alpha particle as a particle in a "box" – the nucleus – and calculate the…
Thorondor
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In Fermi's Golden Rule, does the transition probability increase linearly with time or quadratically with time?
When deriving Fermi's Golden rule, we get that the probability of a quantum system transitioning from an initial state $|i\rangle$ to a final state $|f\rangle$ is
$$P_{i\rightarrow…
SalahTheGoat
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