How do you mathematically describe wave function overlap?

In summary, the conversation discusses the concept of wave functions and their relationship to the space where particles can exist. It is asked if there is a way to mathematically describe this space and determine the time period at which the overlap of wave functions will occur. It is clarified that there is nothing special about overlapping wave functions and that the equations of quantum mechanics can be used to determine this time period. The conversation also addresses misconceptions about the role of wave functions in describing the space where particles exist and suggests further reading for clarification.
  • #1
Zachary Nichols
15
0
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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  • #2
Wave functions from what?
There is nothing special about overlapping wavefunctions.
Zachary Nichols said:
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.
 
  • #3
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
 
  • #4
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.
Zachary Nichols said:
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.
 
  • #5
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
 
  • #6
Zachary Nichols said:
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
 

Related to How do you mathematically describe wave function overlap?

1. What is wave function overlap?

Wave function overlap is a mathematical concept that describes the degree of similarity between two quantum wave functions. It is a measure of how much two wave functions overlap in space and time.

2. How is wave function overlap calculated?

Wave function overlap is typically calculated using the integral of the product of the two wave functions. This is known as the inner product or overlap integral and is denoted by the symbol <Φ|Ψ>.

3. What does a high wave function overlap indicate?

A high wave function overlap indicates a high degree of similarity between the two wave functions. This means that the two quantum systems described by the wave functions have a high probability of interacting and influencing each other.

4. Why is wave function overlap important?

Wave function overlap is important because it is a fundamental concept in quantum mechanics and plays a crucial role in determining the behavior and properties of quantum systems. It is also used in various calculations and predictions in the field of quantum physics.

5. How does wave function overlap relate to quantum entanglement?

Wave function overlap is closely related to quantum entanglement, which is the phenomenon where two or more quantum particles become connected in such a way that the state of one particle affects the state of the other(s). High wave function overlap is necessary for entanglement to occur between two particles.

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