Explicit Euler method for solving time dependent Schr\H{o}dinger equation

Using an explicit Euler substitution it was obtained a system of differential equations, which can be used to find the solution of time-dependent 1-dimentional Schr\H{o}dinger equation for a general form of the time-dependent potential.Comment: 1 page. Accepted for publication in Phys. Rev.

Classes of exact wavefunctions for general time-dependent Dirac Hamiltonians in 1+1 dimensions

In this work we construct two classes of exact solutions for the most general time-dependent Dirac Hamiltonian in 1+1 dimensions. Some problems regarding to some formal solutions in the literature are discussed. Finally the existence of a generalized Lewis-Riesenfeld invariant connected with such solutions is discussed

Ultrasonic pulse propagation in inhomogeneous one-dimensional media

The propagation of acoustic or ultrasonic pulses and waves in 1-D media with continuous inhomogeneities due to spatial variations in density, Young modulus, and/or cross section of the propagation medium is discussed. A semianalytical approach leads to a general form of the solution, which can be described by a function, whose Taylor expansion is absolutely convergent. The special case of a periodic inhomogeneity is studied in detail and the dispersion law is found. It is also shown that a finite width pulse is generally not broken down by the inhomogeneity, even though its law of motion is perturbed. A numerical treatment based on the Local Interaction Simulation Approach (LISA) is also considered, and the results of the simulations compared with the semianalytical ones. (C) 1998 Acoustical Society of America. [S0001-4966(98)00807-8]