Replusz said:
I agree with George. Focus on your ##e^{i H_0 t}## which you turned into ##e^{-i E_m t}##.Replusz said:
nrqed said:
Yes, this is correct.Replusz said:
Fermi's golden rule is a fundamental principle in quantum mechanics that describes the transition rate between two quantum states. It states that the transition rate is proportional to the square of the matrix element of the perturbation between the initial and final states.
The derivation of Fermi's golden rule can be hazy because it involves complex mathematical concepts and equations that may be difficult to understand without a strong background in quantum mechanics and mathematics. Additionally, there are multiple approaches to deriving the rule, which can lead to confusion.
One common misconception about Fermi's golden rule is that it only applies to simple systems and cannot be used for more complex systems. However, the rule can be applied to a wide range of systems, as long as the perturbation is small enough.
Another misconception is that Fermi's golden rule only applies to transitions between discrete energy levels. In reality, it can also be used to describe transitions between continuous energy levels.
To better understand the derivation of Fermi's golden rule, it is important to have a strong understanding of the underlying mathematical concepts and equations involved. It can also be helpful to consult multiple sources and seek guidance from a knowledgeable instructor or mentor.
Fermi's golden rule has many practical applications in physics, chemistry, and engineering. It is commonly used to study the rates of chemical reactions, the behavior of electrons in materials, and the emission and absorption of radiation. It is also used in the development of quantum technologies such as quantum computing and quantum cryptography.