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Pré-Publication, Document De Travail Année : 2021

Clarifying issues about rotational motion in classical and quantum mechanics

Résumé

It is proved in physics textbooks that angular frequencies can be treated as vectors. However this is subject to a caveat that in general is not pointed out, and this can lead to confusion. We also point out that the textbook interpretations of the angular-momentum and spin operators in quantum mechanics are wrong. E.g.Lz = ı (x ∂ ∂y − y ∂ ∂x) is not the general expression of the operator for the z-component Lz of the angular momentum L, but the expression of the operatorL for the angular momentum L when it is aligned with the z-axis. Hence it corresponds to a full vector quantity L rather than to a scalar component Lz. The same applies mutatis mutandis for the spin operators. With the correct interpretations the conceptual difficulties we encounter in making sense of angular momentum in quantum mechanics disappear, such that it is no longer mysterious. The change of interpretation has no impact on the algebraic results, such that they remain in agreement with experimental data. It is just a matter of the correct geometrical meaning of the algebra. All these statements are proved within the framework of the group theory of SU(2) which is the basic language on which descriptions of rotational motion in quantum mechanics are founded.
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Dates et versions

hal-03323780 , version 1 (23-08-2021)
hal-03323780 , version 2 (11-09-2021)
hal-03323780 , version 3 (09-06-2022)
hal-03323780 , version 4 (16-06-2022)
hal-03323780 , version 5 (28-06-2022)

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  • HAL Id : hal-03323780 , version 1

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Gerrit Coddens. Clarifying issues about rotational motion in classical and quantum mechanics. 2021. ⟨hal-03323780v1⟩
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