Superposition principle and continuity

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Discussion Overview

The discussion revolves around the relationship between the superposition principle and the continuity of the wave function (ψ) in the context of potential barriers. Participants explore how the superposition principle may be used to demonstrate the continuity of ψ, particularly in quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how the superposition principle can be used to prove the continuity of ψ in potential barriers.
  • Another participant points out that a discontinuous wave function cannot satisfy the Schrödinger equation due to the lack of a spatial derivative, suggesting this is independent of superposition.
  • There is a request for clarification on the requirement of proving continuity "by superposition," with a note that since ψ satisfies the Schrödinger equation, it should be differentiable and thus continuous.
  • A later reply references the linearity of the Schrödinger equation and the definition of the superposition principle, implying a connection to the continuity of ψ.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and relevance of the superposition principle in proving the continuity of ψ. The discussion remains unresolved, with multiple competing perspectives on the topic.

Contextual Notes

Some participants highlight the need for context regarding the question, while others emphasize the mathematical properties of the wave function in relation to the Schrödinger equation.

sciboudy
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hello
i have question : how the superposition principle proves continuity of ψ in potential barrier
 
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and how to prove the continuity of psi
 
Does this question have any context? Book/paper/whatever?
A discontinuous wave function cannot satisfy the Schroedinger equation (it does not have a spatial derivative), but this has no clear relation to superposition. And it is independent of any explicit potentials.
 
okay ... but how to prove continuity of psi by super position ? example in potential barrier
 
sciboudy said:
okay ... but how to prove continuity of psi by super position ? example in potential barrier
I don't understand the "by superposition" requirement. Since ψ satisfies the Schrödinger equation, it's differentiable, and every differentiable function is continuous.
 

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