Linked Questions
19 questions linked to/from Interpretation of "transition rate" in Fermi's golden rule
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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| i\...
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5
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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 ...
- 797
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4
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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 ...
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3
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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
13
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answer
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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:
$$ P_{f \leftarrow i}(t) = |\langle f|V|i\rangle|^2 \frac{4\...
- 2,654
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1
answer
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When does the Fermi golden rule break down?
It is widely used in all fields of physics. However, how accurate is it? It seems that many people use it without estimating its accuracy. When does it break down? Any example?
- 2,165
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Fermi's golden rule and infinite probablity?
I am slightly confused about the application of Fermi's golden rule. Which during standard derivations indicates a probability of transitioning from the state $|i \rangle$ to the state $|f\rangle$ of:
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5
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2
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In Fermi's Golden Rule, does the transition probability increase linearly with time or quadratically with time?
When deriving Fermi's Golden rule, we get that the probability of a quantum system transitioning from an initial state $|i\rangle$ to a final state $|f\rangle$ is
$$P_{i\rightarrow f}(t)=\frac{|V_{fi}|...
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2
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1
answer
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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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5
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1
answer
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Rate in Fermi's golden rule
There is a very clear derivation of Fermi's golden rule (actually Dirac's) here. Everything runs smoothly until, somehow, the equivalence
$$
\Gamma_{a \rightarrow b} = \frac{P_{a \rightarrow b}}{t}
$$...
- 643
4
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1
answer
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Fermi Golden Rule
First order time dependent perturbation theory tells us that under the influence of a perturbation $Ve^{i\omega t}$, a system that started in the state $|n\rangle$ at time $t=0$ has probability $$P_k(...
- 1,229
1
vote
2
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630
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Probability density in Fermi golden rule
Consider Fermi golden rule
$$\Gamma _{{i\rightarrow f}}={\frac {2\pi }{\hbar }}\left|\langle f|H'|i\rangle \right|^{{2}}\rho $$
I don't understand why $\left|\langle f|H'|i\rangle \right|^{{2}}$ is ...
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1
vote
2
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Why does a "constant" perturbation favour the transition at $\omega_{fi}=0$?
For a constant perturbation of the form $$\hat{H'}(t)=\hat{V}\theta(t)$$ to a time-independent Hamiltonian $\hat{H}_0$, the transition probability at time $t$ from an eigenstate $|i\rangle$ of $\hat{H}...
- 12.3k
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1
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Fermi's golden rule and Fock states
I am having trouble understanding the derivation of the rate of spontaneous and stimulated emission given in this link.
We have a perturbation that takes the form:
$$ \hat H=\sum_{\vec k}f(\vec r,\...
1
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2
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Why do we need large time assumption for energy conservation in electron transitions?
For electron absorption calculations (with an electric field perturbation $\Delta H = eE_0x \cos(\omega t)$) we end up with an integral like:
$$c_2(t) \propto \int \rho(\omega) \left( \frac{\sin(\...
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vote
1
answer
753
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Correlation Amplitude in QM
The following is a section "Correlation Amplitude and the Energy-Time Uncertainty Relation" from Sakurai's Modern Quantum Mechanics book page 79:
Question:
Why does it state that the oscillations ...
user100411
1
vote
2
answers
607
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Dirac-delta function in Derivation of Fermi's Golden Rule
I was following along Mark Thomson's Modern Particle Physics, and got stuck on this book's derivation of Fermi's Golden Rule (On page 53):
"...
If there are d$n$ accessible final states in the ...
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1
answer
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Feynman, Hibbs Perturbations and Energy
I am currently self-studying from Feynman & Hibbs’ Quantum Mecahnics and Path Integrals, but having an issue understanding a step in their development of first-order perturbations. They define
$$...
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1
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1
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State transition (continuum)
If we assume that because of factors, a quantum mechanical system needs to rearrange itself, and in doing so, it might change it's state, to another one. In our consideration, we tried to find the ...
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