What is a wave function and how does it describe the wave nature of a particle?

[janakiraman]

What is exactly a wave function of the system. I have been told that wave function is something that is used to describe the wave nature of a particle but how? I could not understand or rather visualize it.

And how can the wave function be a complex number or a negative value? For example if the probability for an atom or electron to be in a particular position is 0.25, the wave function can be -0.5 or +0.5. Under what conditions would the wave function have +0.5 or -0.5? And under which conditions can it have a complex value

P.S: I don't know most of the quantum mechanics jargons and words, so I would be happy if you can try to explain your replies in simple layman terms.

 

[Avodyne]

Found by googling "what is a wave function":

http://underdown.wordpress.com/2006/09/18/what-is-a-wave-function

 

[janakiraman]

@ Avodyne

thank you very much for the link. Well precisely this is the information i had before posting the query. My question is can anyone state a simple example by which we can define a wavefunction for a particular object. Also if the system and its probability density is provided, can we find out the wavefunction based upon those data

 

[mrandersdk]

you can't understand wavefuctions without reading about quantum mechanics, because to understand the wavefunction you need to understand what quantum mechanics is about. The wave function comes from solving the schrödinger equation and then there are interpretations of the wavefunction. But if you want to understand then read griffiths introduction to quantum mechanics.

And by the wave given the systems probabillity density (if that makes sense at all), you can't find the wavefunction because you only know |wavefunction|^2, so you don't know the complex phase.

It seemse to me that you are trying to understand QM from what you know about classical physics, you shouldn't do that.

 

[malawi_glenn]

Just to add to the latest answer= the wave function can obtain both complex and negative values since the probability is given by the modulus square of the WF. Wavefunction is the probability DENSITY, squaring a density gives you the observable. We have many old threads about this topic, try to search and read those.