How do you mathematically describe wave function overlap?

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Discussion Overview

The discussion focuses on the mathematical description of wave function overlap, particularly in the context of quantum mechanics and hydrogen orbital wave functions. Participants explore the implications of overlap in terms of particle existence and randomness, as well as the potential to determine time periods for such overlaps.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant inquires about the mathematical description of the space where wave functions overlap and whether it can indicate the time period of that overlap.
  • Another participant questions the significance of overlapping wave functions, suggesting that there is nothing inherently special about them and refers to quantum mechanics equations for determining overlap timing.
  • A participant specifies that the discussion pertains to hydrogen orbital wave functions and suggests that overlap indicates a state of randomness for a particle shifting between states until observation collapses the wave function.
  • Another participant counters that in normal hydrogen, the electron is typically in the ground state, implying that other states are irrelevant to the discussion of overlap.
  • A participant seeks clarification on what represents the space of randomness between two states, emphasizing that wave functions describe potential particle locations.
  • One participant reiterates the idea of randomness and overlap but is met with disagreement, suggesting misconceptions about wave functions.

Areas of Agreement / Disagreement

Participants express differing views on the significance and interpretation of wave function overlap, with no consensus reached on the implications of randomness or the relevance of specific states in hydrogen.

Contextual Notes

Some assumptions about wave function interpretation and the nature of randomness in quantum mechanics remain unresolved. The discussion also reflects varying levels of understanding regarding the role of wave functions in describing particle states.

Zachary Nichols
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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.
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.
 
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
 
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.
 
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
 
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
 

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