Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

This is the problem I want to share with you.

We have the hamiltonian H=aP+bm, which we are commuting with the position x and take:

[x,H]=ia, (ħ=1)

Ok. Now if we take, instead of x, the operator

X=Π_{+}x Π_{+}+Π_{-}xΠ_{-}

where Π_{±}projects on states of positive or negative energy

the result will be:

[X,H]=iP/H

Can somebody explain me how this result comes out.

Thanks in advance

QC

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# Commuting Hamiltonian with the projection of position

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