What the wave function exactly mean?

[angadaria]

hi guys, i wanted to know what the wave function exactly mean?and what is the physical interpretation of wave function?

 

[jtbell]

hi guys, i wanted to know what the wave function exactly mean?

The "absolute square" of the wave function, $\psi^*\psi$ (keep in mind the wave function is generally complex, not real), is the probability density for finding a particle at a particular location. The probability of finding the particle in a particular region of space is

$$P = \int {\psi^*\psi} dxdydz$$

where the limits of integration specify the boundaries of the region.

and what is the physical interpretation of wave function?

There is a lot of disagreement about this, and several different viable theories about the interpretation of the wave function. Unfortunately, it is not possible to distinguish between these interpretations because they all predict the same results for experiments that we can actually (even in principle) perform.

 

[angadaria]

thanks for the reply...what do we mean when we say $$\Psi$$ (x,t)?

 

[jtbell]

what do we mean when we say $$\Psi$$ (x,t)?

The wave function depends on position and time. To expand on my answer a bit, the probability that a particle is located in a certain region of space varies with time, in general:

$$P(t) = \int {\Psi^*(x,t) \Psi(x,t) dx$$

(ignoring the y and z dimensions)

 

[dextercioby]

In nonrelativistic mechanics, x and t are independent variables in the sense that a point P in a 1-D configuration's space is parametrized by the coordinate x at any value of time "t". In Quantum Mechanics, x is promoted to an observable (actually t can be promoted to an observable, too, but this is not universally accepted, so it's not really textbook material) and its spectral values can be used to parametrize the space of wavefunctions. The <t> is a parameter as well.