In summary, the conversation discusses the concept of imaginary potential energy and its use in numerical calculations, particularly in quantum systems. The idea is a computational trick and can be used to calculate the ground state of a system. There is also mention of the Wigner-Weisskopf approximation, which is used to understand decay, and a link to a clear derivation on the topic.
Griffith says in problem 1.15 the potential energy has an imaginary part. my question is that any real case exists where the part of the potential energy is imaginary?
Measurable physical quantities like energy can never be complex numbers. The thing described there is just a computational "trick". A similar effect can be produced by setting a complex mass or time variable. This can be used in the numerical calculation of the ground state of a quantum system, as I have done in this blog post of mine: https://physicscomputingblog.com/20...art-5-schrodinger-equation-in-imaginary-time/
Sigh :-(. Is this again from Griffiths's QM textbook? I cannot understand how an expert of the subject can be so sloppy and confusing for students. That's the more ununderstandable since he's obviously a brillant teacher of physics, as one can get from reading is electromagnetics textbook and many articles in AJP.
To understand "decay", particularly the exponential-decay law (which is necessarily an approximation only), you need to consider time-dependent perturbation theory. The standard treatment is known as Wigner-Weisskopf approximation. Here's a very clear derivation on the example of spontaneous emission, but it's of course applicable very generally
Sigh :-(. Is this again from Griffiths's QM textbook? I cannot understand how an expert of the subject can be so sloppy and confusing for students. That's the more ununderstandable since he's obviously a brillant teacher of physics, as one can get from reading is electromagnetics textbook and many articles in AJP.
To understand "decay", particularly the exponential-decay law (which is necessarily an approximation only), you need to consider time-dependent perturbation theory. The standard treatment is known as Wigner-Weisskopf approximation. Here's a very clear derivation on the example of spontaneous emission, but it's of course applicable very generally
