Ladder Operators and Dirac as the source.

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Discussion Overview

The discussion centers around the historical introduction of creation and annihilation operators, also known as ladder operators, by Paul Dirac in the context of the quantum harmonic oscillator. Participants seek to identify specific sources, such as papers or books, where Dirac presented these concepts.

Discussion Character

  • Historical, Meta-discussion

Main Points Raised

  • One participant inquires about the specific source where Dirac introduced creation and annihilation operators.
  • Another suggests looking into "Modern Quantum Mechanics" by Sakurai as a potential reference.
  • A participant notes that Dirac's "Principles of Quantum Mechanics" from 1930 discusses the use of raising and lowering operators, specifically referencing page 136.
  • There is a request for confirmation of the page number from the first edition of Dirac's book.
  • A participant acknowledges that while section 41 of the first edition is titled "The Harmonic Oscillator," the text is not available online.
  • One participant comments on the context of ladder operators being meaningful only within the bra-ket formalism introduced by Dirac, noting the absence of prior printed versions of this formalism.
  • A later reply suggests a consensus that Dirac introduced these operators in his textbook on Quantum Mechanics.

Areas of Agreement / Disagreement

While there is a general agreement that Dirac introduced the operators in his textbook, the specific details and sources remain somewhat unresolved, with participants discussing various editions and contexts.

Contextual Notes

There are limitations regarding the availability of specific texts and editions, as well as uncertainty about the first instances of the bra-ket formalism in other textbooks.

TheShrike
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Hello,

I've read that Dirac introduced the idea of the creation and annihilation operators in the solution to the quantum harmonic oscillator problem, but can anyone tell me where he did this? In a paper, or maybe in a book?

I've had a little search online, but I've yet to discover anything, so I thought I'd check the PF collective in case anyone knew off the top of their head.
 
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you may try 'modern quantum mechanics' by sakurai.
 
The use of raising and lowering operators to solve the harmonic oscillator goes back at least as far as 1930, "Principles of Quantum Mechanics" by Dirac. See here, on p136.
 
Hi Bill, your link is to the 4th edition. One must provide us with the same page (if the same page) from the 1st edition of 1930.
 
Sorry, you're right. The best I can do is confirm that section 41 of the 1st edition is entitled "The Harmonic Oscillator", however the text of it does not seem to be available online.

(:eek: copies of the 1st edition sell for ~ $1500!)
 
Well, ita, itabar operators make sense only in the bra-ket context and there is no printed version of the bra-ket formalism before his 1930 book (?). Actually, I'm not sure which was the first textbook by another author copying Dirac's bra-ket treatment, but that of course after 1930, perhaps 1940.
 
Consensus seems to be that Dirac introduced them in his textbook on Quantum Mechanics. Ok, cool, thanks very much people.
 

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