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May be a trivial question. But, "Why angular momentum is an important physical quantity in quantum mechanics?".

Could anyone explain me?

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- #1

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May be a trivial question. But, "Why angular momentum is an important physical quantity in quantum mechanics?".

Could anyone explain me?

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CompuChip

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In quantum mechanics, angular momentum is particularly important, because the same mathematical formalism that describes "real" angular momentum (a particle spinning around an axis) also turns out to describe some other

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Although, care needs be taken over that characterisation. Spin certain does contribute to the angular momentum of the system --- see the Einstein-de Hass effect. Furthermore, we know that neither spatial angular momentum (L) or spin (S) alone is a symmetry of the universe, but that the combined J is.In quantum mechanics, angular momentum is particularly important, because the same mathematical formalism that describes "real" angular momentum (a particle spinning around an axis) also turns out to describe some otherinternaldegree of freedom (which we, confusingly, callspin) which is also extremely important.

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For consistency, these groups are the symmetry groups of the system (e.g., the rotation group), and one of the most important features steps in the development of quantum mechanics was the (re)discovery of groups. If you knew the symmetries of a system, you could already tell a lot about it, like selection rules, degeneracy, etc., without really "solving" anything. Different systems with the same symmetries look very much the same.

For systems with rotational symmetry, states come in representations of the rotation group SO(3), and these representations are labeled by quantum numbers which also happen to correspond to angular momentum eigenvalues. But they are very general. Try to solve for the electromagnetic field of some localized current distribution (a problem that has nothing to do with quantum mechanics) and the same "quantum numbers" will appear in the spherical harmonic functions.

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malawi_glenn

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Adding: Energy levels of certain systems, look for instance on the Nuclear Shell model.

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