Need Help (not Homework question)

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Discussion Overview

The discussion revolves around the derivation of the Heisenberg Uncertainty Principle (HUP) and the Schrödinger Equation (SE) using the commutator of position and momentum operators in quantum mechanics. Participants seek clarity on these derivations and share resources related to them.

Discussion Character

  • Technical explanation
  • Homework-related
  • Meta-discussion

Main Points Raised

  • One participant requests a clear derivation of the HUP and the Schrödinger Equation from the commutator of position and momentum operators.
  • Another participant plans to write the derivations in LaTeX, indicating these are common requests.
  • A participant mentions that the derivation can be found in Sakurai's textbook, noting a relationship between the uncertainties of conjugate operators and their commutator.
  • Another participant suggests that derivations are available in almost any quantum mechanics textbook.
  • A participant expresses difficulty finding specific derivations in their quantum textbook and inquires about the LaTeX work.
  • One participant recommends Sakurai's "Modern Quantum Mechanics" as a comprehensive resource, while also suggesting Ballentine's book for foundational understanding.
  • A participant shares a link to a library item related to the HUP and mentions that they will work on the Schrödinger Equation next weekend.
  • There are references to older threads discussing the derivation of the Schrödinger Equation, suggesting that additional resources may be available.

Areas of Agreement / Disagreement

Participants generally agree that the derivations can be found in established quantum mechanics textbooks, but there is no consensus on the availability of specific derivations in the textbooks referenced by the participants. The discussion remains unresolved regarding the clarity and accessibility of these derivations.

Contextual Notes

Some participants express uncertainty about the specific content of their textbooks and the derivations they contain, indicating a potential limitation in the resources available to them.

Cluelessluke
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Hey everyone. I would love for someone to show me quite clearly how to derive [tex]\Delta[/tex]x[tex]\Delta[/tex]p[tex]\geq[/tex][tex]\frac{\hbar}{2}[/tex] and separately how to derive the Schrödinger Equation both from using the [x,p] commutator. With [tex]\hat{x}[/tex]=i[tex]\hbar[/tex][tex]\frac{\partial}{\partial p}[/tex] and [tex]\hat{p}[/tex]=p (in momentum space). Thanks in advance for anyone's help!
 
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i am actually planning to write both those derivation in LaTeX tomorrow, since those are very frequently asked questions.
 
Awesome! Thanks so much. If it wouldn't be too much to ask, maybe you could post a link to it in this thread? Thanks again!
 
The derivation can be found in Sakurai. There is an equation relating the product of the uncertainties of two conjugate operators to the commutator of the operators. Substituting the [x,p] commutator yields the HUP.
 
the derivations can be found in almost any QM textbook
 
So I looked throughout my quantum textbook but there is not a derivation of these two processes specifically in there. malawi_glenn, I was wondering if you were able to LaTeX those fellas yet or not. Thanks for your time.
 
which book do you have? I have sakurai - modern QM, and it derives both HUP and SE. In my opinion, it is THE quantum mechanics textbook. But since it is dealing with a second course in QM, it requires "the basics" so in that opinion "Quantum Mechanics - a modern development " by ballentine is better, but if you can a copy of sakurais book - you have everything you need.

Well we got some library items done on the HUP atleast, shrödinger will be next weekend.

There are a lot of old threads regarding the derivation of SE, you can search for those meanwhile.

This is the item I did, https://www.physicsforums.com/library.php?do=view_item&itemid=207 you perhaps need to study the three first items under "see also" (to the right) which I also did.

Enjoy, and please tell me/us is a step which you can't understand.
 

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