Wednesday, 20 September 2017

quantum mechanics - What are the units of the creation and annihilation operators?


The creation and annihilation operators - also known as ladder operators are; ˆa and ˆa respectively.



Using the equation ˆH=ω(ˆaˆa+12)


and knowing that the units of ˆH are J,


the units of ω are Rad/s



and the units of are J.s


I think that the ladder operators should have units of 1Rad



But I have never seen a square root of an angle in units before. Is this correct?



Answer



The units of are in fact J.s/rad. (thanks AV23) this is because =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.


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