Questions tagged [fermis-golden-rule]

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Fermi Golden Rule: Why interaction picture is fundamental for proving it? [closed]

Sakurai and Wikipedia proove the golden rule in the interaction picture. As the reason of that choice is not clear for me, I ask you what are the difficulties that rise up when you try to get the rule ...
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How to compute the Auger transition rate?

I've been working on computing the Auger transition rate for an exotic atom, one where an electron has been replaced by a particle of arbitrary mass and (integer) charge. I've been closely following ...
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What is a cross section, really? [closed]

Upon looking at different resources, there is a common definition of a cross section (in the context of QFT) to be the probability that some scattering process occurs. For example, here is a ...
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How does transition rate behave under $T \rightarrow \infty$ limit

I am supposed to learn Fermi's Golden Rule, and the book I am using for that is Modern Particle Physics by Mark Thomson. On page 52, he goes : The transition rate $d\Gamma_{fi} = \frac{1}{T}|{T_{fi}^...
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Fermi's golden rule approximations

The derivation of Fermi's golden rule uses the following approximations: Transition time is small. Photon frequency $\omega\approx\omega_f-\omega_i$. The question is, are there any experiments ...
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An instance of the equality of the transition rates $W_{i\to f}$ and $W_{f\to i}$ from Fermi's Golden rule

Fermi's Golden Rule tells that for a perturbing Hamiltonian $\hat{V}$ that couples initial state $\left| i \right\rangle$ to final state $\left| f \right\rangle$, the transition probability per unit ...
Solidification's user avatar
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Transition possibillity rate of infinite well [closed]

Can the standard form of the Fermi golden rule be used to solve part (1) of this problem? The standard form for a two state system is \begin{equation*} \Gamma_{i\rightarrow f} =\frac{2\pi}{\hbar}|\...
Uiupiot's user avatar
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Constant perturbation in Time dependent perturbation theory

I was reading the topic of Time dependent perturbation theory by Nouredine Zettili book. In that for a constant perturbation and after evaluating the probability from initial to final state a factor ...
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DOS in Fermi Golden Rule

I was reading second chapter of Introductory Nuclear Physics by Kenneth S.Krane, and in that chapter he was giving about the logic of why there must be a factor of $\rho(E_{f})$ in the decay ...
Anshul Sharma's user avatar
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1 answer
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Forbidden vs. allowed transitions

In Chapter 1 of his Semiconductor Devices text, Sze gives a crash course (being generous) on solid state physics. At one point, Sze talks about two classes of transitions: Allowed direct Forbidden ...
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Quantum Mechanics - does a paired transition need a perturbation?

I'm doing some theory (to model a device) which, with a bunch of simplifications, wants to consider carrier transitions between extended states in a generalised semiconductor. In particular I'm after ...
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Dirac 4-current for orbital transition

The conserved 4-current is defined as $j^\mu=\bar{\Psi} \gamma^\mu \Psi$ where $\Psi$ is the 4-component wave function. To get the wavefunctions, if we look at the Dirac orbital spinor solution for ...
Jack Zhang's user avatar
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Transition rate

In calculating the transition rate between two levels 1 and 2, most QM textbooks say $$ \left<\psi_2|[x, H_0]|\psi_1\right> = \left<\psi_2|xH_0 - H_0 x|\psi_1\right> = (E_2-E_1) \left<\...
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For a harmonic, time dependent perturbation in QM, how is energy conservation imposed?

I am currently reading Sakurai's Modern Quantum Mechanics, and in the section on time dependent perturbation theory, he derives the first order coefficient for an energy state n at time t in the ...
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Confusion regarding the definition of Fermi's Golden rule

In Wikipedia, the definition starts in the following way: "In quantum physics, Fermi's golden rule is a formula that describes the transition rate (the probability of a transition per unit time) ...
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"Fermi golden rule" approximation in the form $\int_0^\tau dt_1 \int_0^{t_1} dt_2 e^{i\lambda(t_1-t_2)} \approx \tau \frac{i}{\lambda+i0}$

In Eq. (40) of the paper PRB 74, 125319 (2006) (arXiv), the "golden rule approximation" is stated in the form of $$\int_0^\tau dt_1 \int_0^{t_1} dt_2 \: e^{i\lambda(t_1-t_2)} \approx \tau \...
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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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Averaging transition rate for absorption in dipole approximation for unpolarised radiation

The transition rate corresponding to the first-order probability of absorption is given in the dipole approximation as $$W_{ba}=\frac{dP_{ba}^{(1)}}{dt}=\frac{\pi I(\omega_{ba})}{\hbar^2 c \...
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Harmonic perturbation in interaction of radiation with quantum system; making sense of approximation of the integral

In the chapter "The interaction of quantum systems with radiation" (Quantum physics book by Bransden and Joachain, 2nd edition) section 11.2 "Perturbation Theory for harmonic ...
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Confusion regarding Fermi's golden rule

The Fermi Golden Rule is: $$\Gamma_{i\to f}=\frac{2\pi}{\hbar}|\langle f|H'|i\rangle|^2\rho(E_f)$$ In this equation, $|\langle f|H'|i\rangle|$ is giving information about the coupling. However, $f$ ...
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Question about $\delta$-function in Fermi's Golden Rule

I am aware that Fermi's Golden Rule states the rate $k_{if}$ of a process which moves a quantum system from an initial state $i$ to a final state $f$ can be expressed as $$\frac{2\pi}{\hbar}|V_{if}|^2\...
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Volume in a scattering process equal to 1?

I'm studying Fermi's golden rule, and in section 8.3.1 of "Braibant, Giacomelli, Spurio - Particles and Fundamental Interactions" there is an application to the decay of the neutron. While ...
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factor 2pi in golden rule

For the Golden Rule cross-section function, there is a factor $2pi$ in every delta function and a factor of $1/2pi$ for every derivative. Any easy and intuitive way to understand such factors?
liu yang's user avatar
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What is the exact form of the interaction Hamiltonian mentioned in Schwartz's book?

In the book "Quantum Field Theory and the Standard Model" by Schwartz, in eq. (1.24) of chapter 1, he mentions that the interaction Hamiltonian for a particle going from state $i$ to $f$ is ...
Neutralino's user avatar
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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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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 ...
Daniel Waters's user avatar
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Fermi's Golden Rule - Discrete state coupled to a continuum

I'm studying a discrete state coupled to a continuum of states. The Hamiltonian of this interaction, which i called Friedrichs Hamiltonian, is given by: $$H_{F}=E_{e}|e\rangle\langle e|+\int U|\chi_{U}...
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Relation between tunneling current and fermi golden rule (Bardeen model)

I am looking into the paper of Tersoff and Hamann - Theory of the scanning tunneling microscope. In this one there is the tunnel current written as $$I = \frac{2\pi e}{\hbar} \sum_{\mu ,\nu} f(E_\mu) [...
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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 ...
Lost's user avatar
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3 votes
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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 ...
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Calculation of the rate of transition of the Hydrogen electron from $|2lm\rangle$ to ground state

This is how it was calculated in my book: We take the electromagnetic field to be part of the system. The initial state of the system is the direct product $|2,l,m\rangle \times |0\rangle$. $|0 \...
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How is it possible to obtain delta function in the degenerate perturbation theory?

$$H = H_0 + V(t), V(0) = 0$$ Let $|i_0\rangle$ be the eigenstates of $H_0$, i.e. $H_0|i_0\rangle = E_{i_0}|i_0\rangle$, and $|i(t)\rangle$ is $|i_0\rangle$ after a time $t$ (with hamiltonian $H$). If $...
Михаил Игоревич Краснов's user avatar
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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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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 ...
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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 ...
Sahand Tabatabaei's user avatar
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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}...
Solidification's user avatar
1 vote
1 answer
507 views

Fermi's golden rule notation

I am currently reading through Sakurai (1st ed) and he states that Fermi's golden rule can sometimes be written in terms of a Dirac delta function, with the assumption that $$ \rho (E_n) \equiv \delta ...
mathsisu97's user avatar
12 votes
1 answer
724 views

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\...
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Transition rate derivation in non-relativistic quantum scattering

I am reading Principles of Quantum Mechanics by Shankar, here's a derivation I am puzzled. To evaluate probability of particle entering detector in some solid angle, using $S$-matrix and Fermi's ...
wong tom's user avatar
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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(\...
Alex Gower's user avatar
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5 answers
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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 ...
Frederik Ravn Klausen's user avatar
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Why are electromagnetic field modes considered a continuum of states (e.g. in the Fermi Golden Rule calculation)?

When we consider a state transition e.g. from 2p to 1s in the hydrogen atom, the energy gets emitted in the form of a photon. As an assumption underlying the Golden Rule application, we expect an ...
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Getting $\frac{2\pi}{\hbar}$ factor in Fermi's Golden Rule without using limit of no time dependence

Fermi's golden rule is: $$R = \frac{2\pi}{\hbar} |\langle f| \Delta H_0 |i \rangle|^2 \rho(E)$$ and it looks like all derivations of this at some point use the limit of a time dependent perturbation ...
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Does time-dependent perturbation theory work for time-independent perturbations?

Are the results from time-dependent perturbation theory for time dependent Hamiltonians of the form $H = H_0 + \Delta H(t)$ (such as the result below) equally valid for time independent Hamiltonians ...
Alex Gower's user avatar
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Fermi's golden rule, continuuous spectrum

Usually when the Fermi's golden rule is derived using time-dependent perturbation theory, the notation suggests that the system under consideration has discrete spectrum (quantum harmonic oscillator, ...
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Two-body decay conservation of energy

I was trying to derive transition rate for a two-body decay process. In one of the reference I'm following, it consider $a\rightarrow1+2$ decay, and said the daughter particles in center-of-mass ...
Andri jauhari's user avatar
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$N$-body phase space for Fermi golden rule

I was following along Mark Thomson's Modern Particle Physics, and stumble upe the derivation of d$n$ of Fermi golden rule on page 62: "... For the decay of a particle to a final state consisting ...
Andri jauhari's user avatar
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2 answers
509 views

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 ...
Andri jauhari's user avatar
5 votes
3 answers
307 views

Can inelastic scattering still give rise to diffraction?

I am having a conceptual difficulty reconciling inelastic events and diffraction, particularly whether or not you can have inelastic diffraction. Here is my thought experiment that I am working ...
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