Can someone prove the uncertainty principle for me

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Discussion Overview

The discussion revolves around the proof of the uncertainty principle in quantum mechanics, specifically the mathematical formulation and its implications. Participants seek clarity on the principle's derivation and references to relevant literature.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that their textbook states the uncertainty principle without providing a proof, expressing a need for a derivation due to its unintuitive nature.
  • Another participant claims that the uncertainty principle is a consequence of the commutation relations and references Ballentine's book for further reading.
  • A question is raised about the identity of Ballentine, leading to clarification that it refers to the author of a well-known quantum mechanics textbook.
  • Further clarification is provided regarding the full title of Ballentine's book, emphasizing the common practice of referring to authors instead of full titles in the field.
  • Links to external resources related to the uncertainty principle are shared by a participant.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the proof of the uncertainty principle, and multiple references and perspectives are presented without resolving the initial request for a proof.

Contextual Notes

There are limitations in the discussion regarding the specific mathematical steps involved in the proof of the uncertainty principle, as well as the dependence on the definitions of the involved operators.

Maurice7510
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My qm textbook, aptly named "quantum mechanics", is by McIntyre, though it omits the proof for the uncertainty principle and simply states it as ∆A∆B ≥ 1/2|〈[A,B]〉|. In words, if that's unclear, this is 'the product of the rms deviations of A and B is greater than/equal to one half the absolute value of the mean of the commutator of A and B. It says to look elsewhere for the proof, and normally I wouldn't be bothered, but since this leads to Heisenberg's highly unintuitive result, ∆x∆p ≥ h/4π, i feel like a proof is very necessary. If anyone could prove this for me, I'd be very greatful
 
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It's a consequence of the commutation relations. Ballentine covers it in section 8.4.
 
who's ballentine?
 
Ballentine is the author of a quite popular book on quantum mechanics. As all the people writing books on quantum mechanics tend to call their books, "quantum mechanics", too, it has become quite usual to just name the author instead of the title of the book as "the book Quantum Mechanics covers it in section 8.4." would not really be a helpful information.

In this case, the exact name of the book is "Quantum Mechanics -- A Modern Development".
 

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