transition amplitude
A transition amplitude is the complex number that captures the tendency of a system to go from one specific state to another. It is the quantum-mechanical 'connection strength' between a starting state and a destination state, written as an overlap between them after evolution. It is the fundamental quantity from which the chance of the transition is ultimately built.
Like everything in the amplitude layer of quantum mechanics, it is not itself a probability. To turn it into a probability you must take its modulus squared, following the Born rule. The amplitude carries both a size and a phase, and that phase matters enormously: when several routes connect the same start and end, their amplitudes are added first and squared afterwards, so the phases can reinforce or cancel in interference.
This is why amplitudes, not probabilities, are the right currency of quantum dynamics. They obey the linear, wave-like rules of superposition, and only at the very last step — when you ask for an observable chance — do you square them into something real and positive. Transition amplitudes are the building blocks behind scattering cross-sections, decay rates, and the entries of the matrices physicists compute.
The amplitude is the overlap of the evolved initial state with the final state; its modulus squared is the probability.
Never add probabilities when interference is possible; add amplitudes first and square at the end. Skipping straight to probabilities erases the phase information and gives wrong answers for interfering paths.