Ladder Operators and Dirac as the source.

In summary, Dirac introduced the idea of creation and annihilation operators in his 1930 textbook "Principles of Quantum Mechanics" in the section on the Harmonic Oscillator. The use of these operators became a fundamental concept in quantum mechanics and has been adopted by other authors in their textbooks.
  • #1
TheShrike
44
1
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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  • #2
you may try 'modern quantum mechanics' by sakurai.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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!)
 
  • #6
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.
 
  • #7
Consensus seems to be that Dirac introduced them in his textbook on Quantum Mechanics. Ok, cool, thanks very much people.
 

1. What are ladder operators in quantum mechanics?

Ladder operators are mathematical operators used in quantum mechanics to describe the behavior and properties of quantum systems. They are used to describe the transitions between energy levels of a system, and are crucial in understanding the quantization of physical observables.

2. How do ladder operators relate to the Dirac equation?

Ladder operators play a critical role in the formulation of the Dirac equation, which is a relativistic wave equation that describes the behavior of fermions in quantum mechanics. The Dirac equation can be derived from the ladder operators, which represent the creation and annihilation of particles with different spin states.

3. What is the significance of using Dirac as the source in ladder operator methods?

Dirac as the source in ladder operator methods allows for the formulation of a generalized version of the ladder operators that can be applied to any type of quantum system, not just those with spin states. This approach provides a more comprehensive understanding of quantum systems and their properties.

4. How do ladder operators and the Dirac equation help to solve quantum mechanical problems?

By using ladder operators and the Dirac equation, scientists can solve for the energy levels and properties of quantum systems. These mathematical tools allow for the calculation of physical observables, such as energy and angular momentum, which can then be compared to experimental data to validate the theories.

5. Are ladder operators and the Dirac equation still relevant in modern physics?

Yes, ladder operators and the Dirac equation are still widely used in modern physics, particularly in fields such as quantum field theory and particle physics. They remain essential tools for understanding the behavior and properties of quantum systems and have been instrumental in the development of many modern theories and models.

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