schrodingers Ψ?

Question

schrodinger came up with the psi, Ψ , state function.
can you explain what exactly is Ψ and also what the equation Ψ*Ψ = |Ψ|^2 means?

Answer 1

The short answer is that the Ψ represents the square root probability distribution. Just like it took mathematicians a long time to get used to the idea of the square root of negative one (which we now call the imaginary number i), it took physicists a long time to accept the idea of the square root of probability, which is a complex number. The Ψ*Ψ is the actual probability function, which functions pretty much like how Gaussian distributions work, for example. The departure quantum mechanics takes from classical physics is that probability interactions take place in the "probability square root" domain instead of the real one, like what we use to figure out playing card odds. It is for this reason that we run into a lot of quantum weirdness that still fascinates us today.

It might interest you to know that the Schrodinger wave equation is the same as the classical diffusion equation, which describes the random walk in real time, except that instead of real time, imaginary time is substituted in place of real time. It has been speculated by physicists such as Richard Feynman that perhaps the Schrodinger wave equation is some kind of a random walk in imaginary time. There have been a number of papers on this speculation since.