SWKB for the Angular Momentum

SWKB for the Angular Momentum

It has been recently shown [M. Robnik and L. Salasnich, J. Phys. A: Math. Gen., 30, 1719 (1997)] that the WKB series for the quantization of angular momentum L converges to the exact value L = h̄l(l + 1), if summed over all orders, and gives the Langer formula L = h̄(l + 1/2) at the leading order. In this work we solve the eigenvalue problem of the angular momentum operator by using the supersymm...

Angular Momentum

Semiclassical Expansion for the Angular Momentum

The semiclassical method of torus quantization is just the first term of a certain h̄-expansion, usually called the WKB expansion. The method goes back to the early days of quantum mechanics and was developed by Bohr and Sommerfeld for onefreedom systems and separable systems, it was then generalized for integrable (but not necessarily separable) systems by Einstein [1], which is called EBK or t...

Angular Momentum in Chemistry

Noting that current chemical theory is based almost exclusively on electronic energy and spin variables the equal importance of orbital angular momentum is explored in this paper. From its classical definition the angular momentum of electrons in an atom is shown to obey Laplace’s equation, which automatically leads to discrete values in terms of spherical harmonics. This analysis assumes a con...

Rotations and Angular Momentum

2 Exercise. Prove it. ◦ In fact, as sophisticates can show you, on a complex space a linear operator which preserves all norms will also preserve all inner products. But the key thing is to remember is that a unitary operator preserves all inner products (and therefore all norms). • This is analogous to the fact that translations and rotations in ordinary three-dimensional space preserve distan...