Raising and lowering operators

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Discussion Overview

The discussion revolves around the raising and lowering operators for the harmonic oscillator, focusing on their different forms and when each is used. The scope includes theoretical aspects and notation conventions in quantum mechanics.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant expresses confusion regarding the two forms of the raising and lowering operators, specifically their application in different notations.
  • The mathematical expressions for the operators in both function notation and bra-ket notation are presented, highlighting their respective actions on the state functions.
  • Another participant suggests that the choice of notation (bra-ket vs. function notation) influences the application of these operators.

Areas of Agreement / Disagreement

Participants have not reached a consensus, and multiple views regarding the use of notation and the operators' application remain evident.

Contextual Notes

There is a lack of clarity on the specific contexts in which each notation is preferred, and the discussion does not resolve the implications of using one form over the other.

intervoxel
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I'm confused about these two forms of the raising/lowering operators for the harmonic oscillator.
When each one is used?

[tex] a_+\psi_n=i\sqrt{(n+1)\hbar\omega} \psi_{n+1}[/tex]
[tex] a_-\psi_n=-i\sqrt{n\hbar\omega} \psi_{n-1}[/tex]

[tex] a_+|\psi_n\rangle=\sqrt{n+1} |\psi_{n+1}\rangle[/tex]
[tex] a_-|\psi_n\rangle=\sqrt{n} |\psi_{n-1}\rangle[/tex]
 
Last edited:
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what?
 
ansgar said:
what?

Oops! I had pushed the submit button before ending the post. Now it is corrected.
 
it depends if you use bra-ket or "function" notation for your physics.
 

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