- 4.3: Note on Curvilinear Coordinates
- Problems with a particular symmetry, such as cylindrical or spherical, are best attacked using coordinate systems that take full advantage of that symmetry. For example, the Schrödinger equation for the hydrogen atom is best solved using spherical polar coordinates. For this and other differential equation problems, then, we need to find the expressions for differential operators in terms of the appropriate coordinates.
- 4.8: Tensor Operators
- A tensor is a generalization of a such a vector to an object with more than one suffix with the requirement that these components mix among themselves under rotation by each individual suffix following the vector rule. The number of suffixes is the rank of the Cartesian tensor, a rank n tensor has of course 3n components. Tensors are common in physics: they are essential in describing stress, distortion and flow in solids and liquids.
Thumbnail: Hydrogen atom. (Public Domain; Bensaccount).