A Programmed Introduction to Vectors

A Pedestrian Introduction to Gamow Vectors

The Gamow vector description of resonances is compared with the S-matrix and the Green function descriptions using the example of the square barrier potential. By imposing different boundary conditions on the time independent Schrödinger equation, we obtain either eigenvectors corresponding to real eigenvalues and the physical spectrum or eigenvectors corresponding to complex eigenvalues (Gamow...

A Quick Introduction to Vectors, Vector Calculus, and Coordinate Systems

For the present discussion, we define a “coordinate system” as a system for describing positions in space. Any physical law should be expressible in a form that is invariant with respect to our choice of coordinate systems; we certainly do not expect that the laws of physics change when we switch from spherical coordinates to cartesian coordinates! It follows that we should be able to express p...

Introduction: The Philosophy of Vectors

An Introduction to Sociolinguistics

Introduction to circular data

In many diverse scientific fields, the measurements are directions. For instance, a biologist may be measuring the direction of flight of a bird or the orientation of an animal. A series of such observations is called ”directional data”. Since a direction has no magnitude, these can be conveniently represented as points on the circumference of a unit circle centered at the origin or as unit ...