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Orbital Angular Momentum and Group Representations by Clasine van Winter is a Physics and Astronomy article available to read on EtoBox.
What is Orbital Angular Momentum and Group Representations about?
A new approach is presented to the question why in quantum mechanics the orbital angular momentum has integral eigenvalues only. The problem is formulated in terms of linear operators on the Hilbert space Jj of square-integrable functions of the angular variables 9 and cos B. The components of the orbital angular momentum are represented by self-adjoint operators Lj (j = x, y, z) on $j which are constructed starting from the familiar differential operators in terms of 8 and y. The construction is possible in infinitely many ways. These are labeled by a continuous parameter 6, the choice 6 = 0 corresponding to integral eigenvalues. For every particular 6, the operator Zj Lj2 has one and only one extension L2 which is self-adjoint on 5j and such that, for each j, the domain of L2 is contained in the domain of Lj \_ This L2 is the only operator which may represent the square of the orbital angular momentum. It is only in the case 6 = 0 that L2 commutes with each Lj . Also, 6 = 0 is the only case in which the spectra of L, , L, , and L, are the same. These are results which refer directly to the outcome of measurements. It is suggested that this explains why nonintegral eigenvalues for
Who reads Orbital Angular Momentum and Group Representations?
It is typically read by researchers, students, and practitioners in Physics and Astronomy.
- Author
- Clasine van Winter
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0003-4916)
- Published
- 1968
- Language
- EN
- Field
- Physics and Astronomy (Physical Sciences)