quantum probability amplitude

Quantum mechanics is able to predict the result of the two hole experiment by introducing two new rules for calculating probabilities. I read the Wikipedia article on probability amplitude many times over. These rules are not the ones based on everyday experience (see above), but rely instead on something called a "probability amplitude". The scattering matrix. Quantum Amplitude Amplification and Estimation Gilles Brassard∗ Peter Høyer† Michele Mosca‡ Alain Tapp§ 2 May 2000 Abstract Consider a Boolean function χ : X → {0,1} that partitions set X between its good and bad elements, where x is good if χ(x) = 1 and bad otherwise. This approach to the problem of the propagation of quantum particles very superficially compares with the "Path Integral Formulation" of quantum mechanics by Richard Feynman, where the integration over an infinity of possible trajectories is used to compute a "quantum amplitude" [5]. Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born.Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. It has already been mentioned in §75 that a typically stated problem in relativistic quantum theory is to determine the probability amplitudes of various scattering processes (transitions between different states of a system of free particles). L.D. LANDAU, E.M. LIFSHITZ, in Quantum Mechanics: A Shorter Course of Theoretical Physics, 1974 §103. What I understood is that probability amplitude is the square root of the probability of finding an electron around a nucleus, but the square root of the probability does not mean anything in the physical sense.. Can any please explain the physical significance of the probability amplitude in quantum mechanics? Probability Amplitudes.

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