The creation and annihilation operators - also known as ladder operators are; ˆa† and ˆa respectively.
Using the equation ˆH=ℏω(ˆa†ˆa+12)
and knowing that the units of ˆH are J,
the units of ω are Rad/s
and the units of ℏ are J.s
I think that the ladder operators should have units of 1√Rad
But I have never seen a square root of an angle in units before. Is this correct?
Answer
The units of ℏ are in fact J.s/rad. (thanks AV23) this is because ℏ=h2π the units of h are J.s and the units of π are rad. Thus we have J.s/rad. (thanks Noiralef)
Thus the ladder operators are in fact unitless.
On reflection this is the only logical possibility as they move between different eigenstates - which must all be in the same units.
No comments:
Post a Comment