The Wave function (ψ) is central to all quantum mechanics. The wave function has all that we demand about the quantities associated with a particle. But what is ψ exactly?
What the heck is ψ?
For starters, it is a mathematical function associated with the matter waves. Like the waves of light and sound, electric field and pressure are the varying function accounting for their propagation. The matter waves have ψ.
Does wave function have any physical significance?
In short-No. It doesn’t.
The wave function doesn’t have any physical significance because of the way it is defined.
Because the amplitude of the wave can be both negative and positive. It is hard to imagine ψ as a physical quantity. But what is useful is |ψ^2|, the probability density.
The Probability Density ,|ψ^2|
|ψ^2|, Probability density is the probability of finding a particle at particular x,y,x coordinates for a particular given time t.
The probability of finding a particle confined to the x-axis.
Other quantities like position, momentum, and energy can also be determined through rigorous mathematical equations. But we will restrict ourselves to the minimal use of mathematics in our discussions. Hence, the wave function and Probability density are useful in determining various quantities in quantum mechanics.