Carter constant and angular momentum

Angular Momentum

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...

Rotation and Angular Momentum

There is a fundamental connection between the angular momentum (a mechanical quantity) and the rotation operators (which is a symmetry group). The angular momentum is the generator of rotations. Because of this connection, many properties of angular momentum operators can be derived from the properties of the rotation group. We will derive these properties (mainly the commutation relations) sta...

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...

Angular Momentum Diagrams

Starting from the simplest possible building blocks—a ket, a bra, a time-reversed ket, and a time-reversed bra— a diagrammatic formalism is developed for angular momentum coupling problems. The formalism comprises Clebsch–Gordan coefficients as well as 3jm-symbols. The idea of constructing invariants (internal lines) by contracting contragredient pairs of quantities is emphasized throughout. Th...