Question

what is the difference between wavefunction and a wavevector?

Answer 1

@Angu
I think for a wave vector you are referring to the vector k associated with a wave pointing in the direction of propagation and related to the momentum by the equation\[\vec k = 2 \pi \vec p/h\]

A wave function is a function that is a solution the the Schrodinger eq. and carries the information about the possible location of a particle describing its position and time development.

Answer 2

Correct about the wave vector, but I would add that the wave function doesn't carry information about the possible location of a particle. The wave function describes the evolution of the spatial probability distribution associated with that particle.

To simplify, it is impossible to say at any given time, at a given point in space whether or not a particle will be there or not. All one can state is the probability for such an event to occur in a region of space over a given time interval. This is a seemingly minor distinction, but I assure you it is not. The idea is that the particle is truly non-localized and doesn't have any position at all, until one attempts to measure (i.e. look for it/detect it). Only then will the particle be there in that region (where you measure) or not. And all one can say about the measurement, is the probability that particle will be detected over a certain period of time.

So to recap, the wave function can be thought of as a probability distribution that evolves over time. The information it contains can be used to extract probabilities of detecting it in a region of space over a certain period of time.