The Riccati System and a Diffusion-Type Equation

We discuss a method of constructing solution of the initial value problem for duffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-type equation is also considered.Comment: 11 pages, no figure

Exact Wave Functions for Generalized Harmonic Oscillators

We transform the time-dependent Schroedinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time-evolution of exact wave functions of generalized harmonic oscillators is determined in terms of solutions of certain Ermakov and Riccati-type systems. In addition, we show that the classical Arnold transformation is naturally connected with Ehrenfest's theorem for generalized harmonic oscillators.Comment: 10 pages, no figure

A MATLAB program for the computation of the confluent hypergeometric function Φ2

We here present a sample MATLAB program for the numerical evaluation of the confluent hypergeometric function Φ2. This program is based on the calculation of the inverse Laplace transform using the algorithm suggested by Simon and Alouini in their reference textbook [1]