- #1
snoopies622
- 846
- 28
For a simple harmonic oscillator, the creation and annihilation operators can be expressed as linear combinations of the position and momentum operators,
[tex]
\hat {a} = \sqrt { \frac {m \omega} {2 \hbar} } ( \hat {x} + \frac {i \hat {p} } { m \omega } )
[/tex]
[tex]
\hat {a} ^{\dagger} = \sqrt { \frac {m \omega} {2 \hbar} } ( \hat {x} - \frac {i \hat {p} } { m \omega } )
[/tex]
where the position and momentum refer, of course, to the position and momentum of the oscillating particle.
Since creation and annihilation operators also appear when quantizing the electromagnetic field, I was wondering if they can be similarly broken down into [itex] \hat{x} [/itex] and [itex] \hat{p} [/itex] operators, and if these operators correspond to anything physical in this case as well.
[tex]
\hat {a} = \sqrt { \frac {m \omega} {2 \hbar} } ( \hat {x} + \frac {i \hat {p} } { m \omega } )
[/tex]
[tex]
\hat {a} ^{\dagger} = \sqrt { \frac {m \omega} {2 \hbar} } ( \hat {x} - \frac {i \hat {p} } { m \omega } )
[/tex]
where the position and momentum refer, of course, to the position and momentum of the oscillating particle.
Since creation and annihilation operators also appear when quantizing the electromagnetic field, I was wondering if they can be similarly broken down into [itex] \hat{x} [/itex] and [itex] \hat{p} [/itex] operators, and if these operators correspond to anything physical in this case as well.