Can Wave Function Constants Be Both Positive and Negative?

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Discussion Overview

The discussion revolves around the nature of constants in wave functions, specifically whether these constants can take on both positive and negative values. The scope includes theoretical considerations related to quantum mechanics and wave functions, as well as conceptual clarifications regarding their physical interpretation.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether the constants for wave functions can be both positive and negative, noting that their experience has been with positive constants.
  • Another participant explains that wave functions differing only by an overall phase factor represent the same physical state, suggesting that multiplying the constant by -1 does not alter the physics, and that taking the constant to be real and positive is often a matter of convention.
  • A new participant asks why the wave function Ψ (x,y,z) must be square, expressing confusion about the physical meaning of wave functions.
  • In response, another participant references non-contextuality and Gleason's Theorem as a deeper explanation, indicating that this topic requires considerable background knowledge.

Areas of Agreement / Disagreement

Participants express differing views on the nature of wave function constants, with some supporting the idea that they can be negative due to the phase factor argument, while others seem to seek clarity on the foundational aspects of wave functions themselves. The discussion remains unresolved regarding the broader implications of these constants.

Contextual Notes

The discussion includes references to advanced concepts such as Gleason's Theorem, which may not be accessible to all participants, indicating a potential limitation in the shared understanding of the topic.

terp.asessed
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I am curious if the constants for wave functions for a particle in a box can be both +/-...because constants I've applied for wave functions have always been +...
 
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Wave functions that differ only by an overall phase factor ##e^{i \phi}## represent the same physical state, as no observable changes due to this complex phase. Hence, multiplying the constant by ##-1## will not change the physics. Taking the constant to be real and positive is often simply a matter of convention.
 
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Thank you for the explanation!
 
Hi guys,

Just started studying physics hence I obviously have a silly question for you.

Why the wave function Ψ (x,y,z) must be square. It seems wave functions themselves have no meaning if they don't have a physical meaning.

Thanks a lot in advance,
Rodos
 
Thanks Bill. I will check it out.
 

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