X-Nico

5 unusual facts about Good quantum number


Good quantum number

In the case of the hydrogen atom (with the assumption that there is no spin-orbit coupling), the observables that commute with Hamiltonian are the orbital angular momentum, spin angular momentum, the sum of the spin angular momentum and orbital angular momentum, and the z components of the above angular momenta.

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It implies that a physical quantity A is conserved if its Poisson Bracket with the Hamiltonian is zero and it does not depend on time explicitly.

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If the spin orbit interaction is taken into account, we have to add an extra term in Hamiltonian which represents the magnetic dipole interaction energy.

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Systems which can be labelled by good quantum numbers are actually eigenstates of the Hamiltonian.

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If such operators commute with the Hamiltonian, then their expectation value remains constant with time.



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