Angular Momentum Quantization Qualm

Rubén Santamaría

Sami M. Al-Jaber

A. R. Edmonds

Luca Salasnich, F. Sattin

In this paper we prove a recent conjecture about the convergence of the WKB series for the angular momentum operator. We demonstrate that the WKB algorithm for the angular momentum gives the exact quantization formula if all orders are summed. Finally, we discuss the supersymmetric semiclassical quantum mechanics (SWKB), which gives the correct quantization of the angular momentum at the leading order.

Steven M. Pascal

The motion in the angular dimensions described by the solutions in Chapter 14 are related to angular momentum. We explore that relationship in this chapter. This gives insight into the angular TISE, showing that the equation amounts to the classical equation relating angular momentum, moment of inertia, and rotational kinetic energy: KE = L 2 /2I. This also shows that angular momentum is both conserved and quantized in a radial potential. These quantized angular momenta levels are well known to students of chemistry as the orbitals, for which the orbital angular momentum quantum number equals 0, 1, 2, and 3 for the s, p, d, and f orbital, respectively. This quantum number represents the amount of orbital angular momentum of the electron, but the calculation is a little bit more complicated, and is related to the separation constants introduced in Chapter 14 .

Gennaro Auletta, Shang-Yung Wang

In this chapter we shall treat two of the most important observables of quantum mechanical systems: angular momentum and spin. We shall argue that angular momentum is the generator of rotations. In quantummechanics, angular momentum is quantized in units of the reduced Planck constant. The quantization of angular momentum is dealt with by finding the angular momentum eigenvalues and eigenstates. We shall then apply the theory of angular momentum to study the hydrogen atom. Spin is an intrinsic angular momentum of subatomic particles and therefore corresponds to an important intrinsic degree of freedom. We shall discuss briefly how spin was discovered and many of its important properties. Finally, we shall also explore here some further subtleties of quantum theory.a When we consider quantum systems in two or three spatial dimensions, we need to take into account also the effect of rotations. In this case, we need to introduce a physical quantity called the angular momentum, that is, themomentum induced by or connected with rotations. In classical physics the angular momentum of a particle about a given origin is defined by [see Fig. 8.1]