What is the Physical Significance of Various Wave Functions?

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Discussion Overview

The discussion revolves around the physical significance of various wave functions in quantum mechanics. Participants explore the conditions that must be met for a function to be considered a valid wave function, touching on theoretical implications and interpretations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses confusion about the question regarding the physical significance of wave functions and seeks clarification.
  • Another participant questions whether certain functions, such as psi(x) = cos-1 x, can be valid wave functions and asks what conditions must be imposed on wave functions.
  • A different participant suggests that some wave functions must be ruled out, prompting a discussion on the requirements for a function to be interpreted as a physical wave function.
  • One participant proposes that continuity and the property of being a one-to-one function are necessary conditions for a wave function, indicating that these criteria could eliminate some candidates.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which wave functions can have physical significance, and multiple competing views regarding the requirements for valid wave functions remain present.

Contextual Notes

Limitations include the lack of a comprehensive list of conditions for wave functions and the dependence on definitions of continuity and one-to-one functions, which may vary in interpretation.

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Can they all have physical significance though? can for example psi(x) = cos-1 x be a wavefunction? The answer is no, so what conditons are imposed on the wavefunction?
 
mykel_dg said:
All i know is that these wave functions all can have physical significance...
How do you figure? The problem asks you to decide which can have physical significance, so obviously some must be ruled out. What do you think are the requirements for a function to admit an interpretation as a physical wavefunction?
 
I think one of the requirements is that the graph should be continuous, and another requirement is that it shouldn't be a multiple valued function, so it should be a one on one function. With these two requirements, I could rule two graphs.
 

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