A linear theory (quantum theory)?

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Discussion Overview

The discussion revolves around the characterization of quantum mechanics as a linear theory, specifically questioning the criteria that define a theory as linear. Participants explore the implications of linearity in the context of quantum mechanics.

Discussion Character

  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants note that the Schrödinger Equation, which governs quantum mechanics, is a linear differential equation.
  • It is mentioned that a consequence of linearity is that if two solutions, \psi_1 and \psi_2, exist, their sum (\psi_1 + \psi_2) is also a solution.
  • One participant expresses a desire for clarification on how to determine if a theory is linear.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the criteria for defining a theory as linear, and the discussion remains open with differing levels of understanding regarding the implications of linearity in quantum mechanics.

Contextual Notes

Some assumptions about the definitions of linearity and the implications of the Schrödinger Equation may not be fully explored or agreed upon.

xylai
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Some textbooks say that quantum mechanics is a linear theory. I don't know why?
How can we decide a theory is a linear theory?
Thank you!
 
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The governing equation (the Schrödinger Equation) is a linear differential equation. One consequence of linearity is that if \psi_1 and \psi_2 are both solutions, then so is \psi_1 + \psi_2.
 
Thank you!
 

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