Frame of reference for Fermi Golden Rule

In summary, when applying formulas in sub-atomic physics, it is important to use the frame of reference in which the particles are interacting and the frame in which the probe's momentum is measured for accurate results. There is no general rule for choosing a frame, it depends on the specific problem. Good luck!
  • #1
paultsui
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Hi guys. I am currently studying Sub-atomic physics and it seems to me that there are different formulas that work in different frame of reference.

In particular, I would like to ask:

1. Which frame should we use in applying Fermi's Golden Rule? (I've read somewhere that the matrix element is invariant, but I assume the density of states must be frame dependent)

2. The resolution of a probe is defined by its de Broglie wavelength. Once again, this is frame dependent, so which frame should we use to determine a probe's resolution.

3. Is there a general rule of thumb when deciding which frame to use when applying a formula? (It seems to me that most of the problems are done in Zero momentum frame, or is it?)

Thank you so much guysss!
 
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  • #2


Hello there! It's great to see that you are studying sub-atomic physics, it is a fascinating field. To answer your questions:

1. In applying Fermi's Golden Rule, it is important to use the frame of reference in which the particles are interacting. This is because the matrix element, which represents the interaction between the particles, is indeed invariant, but the density of states is frame dependent. So, to get an accurate result, it is necessary to use the frame of reference in which the interaction is taking place.

2. The resolution of a probe is indeed dependent on its de Broglie wavelength, which is determined by its momentum. In this case, it is important to use the frame of reference in which the probe's momentum is measured. This will give you the most accurate resolution for the particular probe.

3. There is no general rule of thumb for deciding which frame to use when applying a formula. It depends on the specific situation and what you are trying to calculate. As you mentioned, many problems are solved in the zero momentum frame, but it is not always the case. It is important to carefully consider the variables and quantities involved in the problem and choose the appropriate frame accordingly.

I hope this helps clarify things for you. Keep up the good work in your studies!
 

1. What is a frame of reference for Fermi Golden Rule?

A frame of reference for Fermi Golden Rule is a mathematical concept used to describe the behavior of particles in a quantum system. It is a set of coordinates and axes used to measure and track the position and movement of particles in the system.

2. How is a frame of reference related to the Fermi Golden Rule?

In the context of the Fermi Golden Rule, a frame of reference is used to determine the initial and final states of particles in a quantum system, as well as the transition matrix elements between these states. This information is crucial for calculating the transition probability and rate according to the Fermi Golden Rule equation.

3. What are the main components of a frame of reference for Fermi Golden Rule?

The main components of a frame of reference for Fermi Golden Rule include the coordinate system, the basis states (usually represented by wavefunctions), and the Hamiltonian operator that describes the dynamics of the system.

4. How does a frame of reference affect the calculation of transition probability in the Fermi Golden Rule?

The frame of reference chosen can greatly affect the calculation of transition probability in the Fermi Golden Rule. This is because different frames of reference may result in different initial and final states, leading to different transition matrix elements and ultimately, different transition probabilities.

5. Are there any limitations to using a frame of reference in the Fermi Golden Rule?

While a frame of reference is a useful tool in understanding and calculating the behavior of particles in a quantum system, it is not always applicable. In some cases, the system may be too complex to be accurately described by a single frame of reference, or the chosen frame of reference may not be the most appropriate for the system being studied.

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