Is it possible to derive HUP from SE?

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Discussion Overview

The discussion centers around the possibility of deriving Heisenberg's Uncertainty Principle (HUP) solely from the Schrödinger Equation (SE). Participants explore the implications of determinism in SE and the nature of uncertainty in quantum mechanics, examining whether the HUP can be established without invoking additional principles or commutation relations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that the HUP can be derived from the commutation relations of coordinate and momentum operators, independent of the SE.
  • Others contend that the deterministic nature of the SE implies it cannot capture the uncertainty required for the HUP, particularly in a one-particle system.
  • One participant suggests that the SE relates to dynamics while uncertainty pertains to kinematics, indicating that the SE does not directly influence the HUP.
  • Another viewpoint posits that the SE is fundamental and historically significant, but questions remain about its sufficiency for deriving the HUP.
  • Several participants discuss the role of basis choice in quantum mechanics, emphasizing that without specifying operators in a basis, the SE cannot be fully utilized to derive the HUP.
  • A later reply outlines a mathematical approach to derive the HUP using properties of the wave function, suggesting that the SE may not be necessary for this derivation.
  • Some participants express uncertainty about the reasoning behind the derivation steps and the implications of the outlined approach.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the HUP can be derived solely from the SE. Multiple competing views are presented, with some asserting that additional principles are necessary while others believe the SE may suffice under certain conditions.

Contextual Notes

Discussions highlight limitations regarding assumptions about the operators involved, the necessity of specifying a basis, and the implications of the SE's deterministic nature. The relationship between dynamics and kinematics in quantum mechanics is also a point of contention.

  • #31
quZz said:
Fredrik, that is quite right... sokrates should realize that Schroedinger equation describes evolution in time, while uncertainty principles are consequences of definitions of corresponding operators. Any solution of Schroedinger equation with Hamiltonian constructed with those operators satisfy uncertainty principles.

: )
Right, I very well realized that thanks to StatusX and Fredrik. It's nailed into my head : )
 
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  • #32
lightarrow said:
Equations means nothing if you don't give specific meanings to the symbols present in there.

I tried very hard to not write a sarcastic answer. But I have to do this:

Oh really?!

(nobody claimed the opposite)
 

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