probability = square of the aplitude?

Question

Does this mean:
amplitude^2 = probability
or
Sqrt(amplitude)=probability

Answer 1

If you're talking about Schrodinger equation, amplitude squared times the interval or volume is probability. You need to include the range of where you are looking. As we said (because the probability function was the latter psi which looks like a pitchfork, the probability is pitchfork squared dx.

Answer 2

If you are referring to a standard probability distribution function, say P(x), then all the amplitude is the point along the distribution where the function is at a maximum, and thus the most probable value over the interval dx. Where you might be thinking of where the square comes into play is the quantum mechanics wavefunction Ψ(r,t). It's not exactly the square as Ψ is actually a complex function, but the wavefunction multiplied by its complex conjugate (Ψ*Ψ) is equal to the probability distribution function of the quantum associated with the wavefunction. Usually for comparison to classical mechanics, the amplitude of this probability distribution function is associated with a fixed value for the property in question.