Transition Rate vs. Probability

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SUMMARY

The discussion centers on the relationship between transition rates and transition probabilities in the context of atomic nuclei. Participants clarify that while transition rates, often represented by Einstein coefficients (Aij, Bij, Bji), are measured in units of s-1, they are fundamentally related to probabilities. Transition probabilities sum to 1, while transition rates quantify the average number of events occurring per unit time. This distinction is crucial for understanding emission and absorption processes between energy levels.

PREREQUISITES
  • Understanding of atomic structure and energy levels
  • Familiarity with Einstein coefficients (Aij, Bij, Bji)
  • Basic knowledge of probability theory
  • Concept of emission and absorption processes in quantum mechanics
NEXT STEPS
  • Research the mathematical relationship between transition rates and probabilities
  • Study the application of Einstein coefficients in quantum mechanics
  • Explore the implications of transition probabilities in spectroscopy
  • Investigate the role of transition rates in nuclear reactions
USEFUL FOR

Physicists, quantum mechanics students, and researchers focusing on atomic transitions and energy level emissions.

AriAstronomer
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Hey everyone,
So I'm doing a bit of research on transition probabilities for a presentation, and it seems like, from checking different resources, that in the atomic nucleus the process of transition rates to describe the rate of emission/absorption between 2 energy levels is used interchangeably with transition probability. I'm not so sure though that they are the same thing, but I'm sure perhaps that they are related.

For instance, some textbooks describe the Einstein coefficients (Aij, Bij, Bji) as measuring transition rates (and it makes sense, I mean the units of them are s-1), but others say they measure probabilities. Are they equivalent, are they simply related, or is it simply different textbooks being lazy and really rates and probabilities are 2 different things?

Thanks,
Ari
 
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They are closely related. Probabilities (by definition) add up to 1. Rates are determined by probabilities and are usually expressed as average number events per unit time.
 

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