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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, ...
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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 ...
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1answer
149 views

Question on doing the integral for Fermi golden rule

Today in the lecture, my professor did something which confused me As an example, we consider the photoelectric effect, in which an electron bound in a Coulomb potential is ionized after ...
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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 ...
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1answer
102 views

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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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 ...
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1answer
190 views

Fermi's Golden Rule

Consider a system with countable quantum states. One can define $J_{ij}$ as the rate of transition of probability from i-th to j-th quantum state. In H-theorem, if one assumes both $$ H:=\sum_{i} p_{i}...
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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}...
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1answer
73 views

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 $$ \Gamma_{a \rightarrow b} = \frac{P_{a \rightarrow b}}{t} $$...
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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 ...
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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}...
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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 $H_c$ ...
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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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1answer
176 views

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(...
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1answer
67 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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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(...
3
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3answers
925 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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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?
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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 ...
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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 ...
5
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1answer
228 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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0answers
51 views

Physical interpretation of Fermi golden rule? [duplicate]

What is the physical interpretation of Fermi's golden rule?
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0answers
63 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| i\...
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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, ...
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5answers
4k 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 ...
2
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1answer
149 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
390 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
382 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 ...
2
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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 ...
5
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3answers
315 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| M_{fi}\right|^2\varrho\...
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1answer
828 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 interactions....
5
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1answer
927 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 ...