Classical counterpart of the quantum |nlm> states

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SUMMARY

The classical counterparts of quantum |nlm> states in an isotropic potential are defined by specific relationships between classical trajectories and quantum states. A classical trajectory with angular momentum L equal to l and energy E equal to E_n corresponds directly to the quantum state |nlm> where the projection m equals L. Furthermore, a classical trajectory can be viewed as a superposition of various |nlm> states characterized by different quantum numbers n, l, and m, with average values of energy and angular momentum represented as and , respectively.

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wdlang
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what are the classical counterparts of the quantum |nlm> states?

in a isotropic potential.

i am reading some books on Redberg atoms and i find this question not so trivial.
 
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wdlang said:
what are the classical counterparts of the quantum |nlm> states?

in a isotropic potential.

i am reading some books on Redberg atoms and i find this question not so trivial.

Roughly speaking, a classical trajectory with the same (big) angular momentum L = l and the same (big) energy E = E_n corresponds to the quantum state |nlm> with the projection m = l=L.

Stricltly speaking, a classical trajectory is a superposition of the states |nlm> with different n, l, and the projections m with E=<E_n>, L = <l>, and the average value of <m>=L.


Bob.
 
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