Recent content by chmodfree

The definition of coherent state $$|\phi\rangle =exp(\sum_{i}\phi_i \hat{a}^\dagger_i)|0\rangle $$ How can I show that the state is eigenstate of annihilation operator a? i.e. $$\hat{a}_i|\phi\rangle=\phi_i|\phi\rangle$$

I mean it maps \dot{Q} from tangent bundle to the real number field as a functional... No problem now, thank you.

Oh I see, that means the contraction P_a\dot{Q}^a is a real.

The smaller the aperture, the greater the depth of field. You can find when taking photo.

According to tunneling effect, there is a certain probability of stationary state electron appear in whole space, even they are in bound state. When the eletron reach the space where Coulomb potential is greater than its stationary state energy, the probability decline exponentially.

Generalized momentum is covariant while velocity is contravariant in coordinate transformation on configuration space, thus they are defined in the tangent bundle and cotangent bundle respectively. Question: Is that means the momentum is a linear functional of velocity? If so, the way to...

You can regard the momentum operator as generator of spatial translation group.