Legendre Polynomials and Angular Momentum

An introduction to Legendre polynomials as precursor to studying angular momentum in quantum chemistry,

The Harmonic Oscillator's Frobenius Solution

The Frobenius solution to the differential equations associated with the harmonic oscillator (QM) is carried out in detail.

Recognizing a Single-Issue Spatial Election

A single-issue spatial election is a voter preference profile derived from an arrangement of candidates and voters on a line, with each voter preferring the nearer of each pair of candidates. We provide a polynomial-time algorithm that determines whether a given preference profile is a single-issue spatial election and, if so, constructs such an election. This result also has preference representation and mechanism design applications.

Laguerre Polynomials, an Introduction

The radial part of the Schrodinger Equation for the H-atom's electron involves Laguerre polynomials, hence this introduction.

Legendre Polynomials, Dipole Moments, Generating Functions, etc..

A standard treatment of aspects of Legendre polynomials is treated here, including the dipole moment expansion, generating functions, etc..

Finite Characterizations and Paretian Preferences

A characterization of a property of binary relations is of finite type if it is stated in terms of ordered T-tuples of alternatives for some positive integer T. A characterization of finite type can be used to determine in polynomial time whether a binary relation over a finite set has the property characterized. Unfortunately, Pareto representability in R2 has no characterization of finite type (Knoblauch, 2002). This result is generalized below Rl, l larger than 2. The method of proof is applied to other properties of binary relations.