How do you mathematically describe wave function overlap?

Is there a way to mathematically describe the space where wave functions overlap like with how wave functions describe the space a particle could exist. Then if that is possible can you determine the time period at which that overlap will occur.
 
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Wave functions from what?
There is nothing special about overlapping wavefunctions.
Then if that is possible can you determine the time period at which that overlap will occur.
Sure, just follow the equations of quantum mechanics.
 
Hydrogen orbital wave functions.

also doesn't the overlap of wave functions represent the space at which the particle is in a state of randomness shifting between the two states until we look at the system and the the overlap collapse into one of the wave functions again
 
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Normal hydrogen has just one electron. Normally, the electron will be in the ground state, and the other states are empty and do not matter.
also doesn't the overlap of wave functions represent the space at which the particle is in a state of randomness shifting between the two states until we look at the system and the the overlap collapse into one of the wave functions again
No.
 
Okay than what does represent that space where a particle is in randomness between two states, because the wave functions only describes the space at which one particle could exist
 
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also doesn't the overlap of wave functions represent the space at which the particle is in a state of randomness shifting between the two states until we look at the system and the the overlap collapse into one of the wave functions again
As Mfb said - no.

But I suspect you have some misconceptions about what a wavefunction is. The following may be helpful in sorting those out:
http://www.scottaaronson.com/democritus/lec9.html

Thanks
Bill
 

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