Quick question on Fermi Golden Rule

In summary, the conversation discusses the relation between momentum and energy, specifically in the case of massless particles. It is noted that the magnitude of momentum is equal to energy for these particles, and the conservation of energy leads to a specific value for the ratio of their momentum and energy. It is also mentioned that the speed of light is taken to be 1 for simplicity.
  • #1
unscientific
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Adopted from my lecture notes, found it a little fishy:

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Shouldn't ##\frac{dp}{dE} = \frac{E}{p}## given that ##p = \sqrt{E^2 - m^2}##. Then the relation should be instead:

[tex]\frac{dp}{dE} = \frac{E}{p} = \frac{E}{\sqrt{E^2 - m^2}}[/tex]
 
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  • #2
Yes, you are right but the problem tells you that B and C are massless. This means that the magnitude of their momenta is equal to their energies. In particular, conservation of energy tells you that ##E_B=E_C=E_A/2## and so ##p_B=p_C=E_A/2##, giving ##dp_B/dE=1/2##.
 
  • #3
Einj said:
Yes, you are right but the problem tells you that B and C are massless. This means that the magnitude of their momenta is equal to their energies. In particular, conservation of energy tells you that ##E_B=E_C=E_A/2## and so ##p_B=p_C=E_A/2##, giving ##dp_B/dE=1/2##.
And I suppose ##c=1##?
 
  • #4
Exactly.
 
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Related to Quick question on Fermi Golden Rule

What is Fermi Golden Rule?

Fermi Golden Rule is a fundamental principle in quantum mechanics that describes the transition rate between two quantum states due to a perturbing Hamiltonian. It is named after Italian physicist Enrico Fermi.

What is the significance of Fermi Golden Rule?

Fermi Golden Rule is important because it helps us understand and calculate the probability of transitions between quantum states, which is essential in many areas of physics, such as quantum optics, solid state physics, and nuclear physics.

How is Fermi Golden Rule derived?

Fermi Golden Rule is derived from the time-dependent perturbation theory in quantum mechanics. It involves calculating the transition matrix elements between the initial and final states, and then taking the square of the absolute value of this matrix element.

What are the assumptions made in Fermi Golden Rule?

The main assumptions made in Fermi Golden Rule are that the perturbing Hamiltonian is small compared to the unperturbed Hamiltonian, and that the perturbation is turned on and off slowly enough so that the system has time to reach a steady state.

How is Fermi Golden Rule applied in practice?

Fermi Golden Rule is applied in a wide range of practical applications, such as calculating the rate of spontaneous emission in atoms, the rate of energy transfer in molecular systems, and the rate of nuclear decay. It is also used in the design of quantum devices and technologies.

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