Can someone give me an Eli5 description of what the matrix element is, particularly in regards to Fermi's Golden Rule?
Fermi's golden rule describes the likelihood of a transition per unit time. Does the matrix element describe the the likelihood of a transition itself without the time element?
Is the matrix element just a variable/operator that facilitates the description of the finite spatial extent of a scattering body?
Or does the matrix element just describe the number of final states available for a given interaction/transition?
The matrix element wiki wasn't very helpful.