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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.

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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

https://www.mpi-hd.mpg.de/personalhomes/palffy/Files/Spontaneous.pdf

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Thank you.vanhees71 said:

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

https://www.mpi-hd.mpg.de/personalhomes/palffy/Files/Spontaneous.pdf

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