Is it possible to derive HUP from SE?

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The discussion centers on whether Heisenberg's Uncertainty Principle (HUP) can be derived solely from the Schrödinger Equation (SE). Participants argue that while the SE is deterministic and fundamental, it lacks the necessary commutation relations to derive the HUP without additional context. The conversation highlights that the uncertainty relation is inherently tied to the properties of operators and the choice of basis, which are not explicitly defined in the SE alone. Some contributors suggest that the HUP can be approached through the properties of wave functions and probability currents, but ultimately conclude that the SE cannot independently yield the HUP without incorporating broader quantum mechanical principles. The consensus is that the SE is insufficient on its own to derive the HUP, emphasizing the need for a complete framework in quantum mechanics.
  • #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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