A fully quantum mechanical methodology for simulating the time evolution of low-dimensional systems in harmonic dissipative environments is presented. The key features of the method are the numerical construction of accurate propagators based on physically motivated reference Hamiltonians and the decomposition of the path integral into a series of shorter time operations, which leads to an iter...

This paper presents a method of numerically computing zeros of an analytic function for the specific application of computing eigenvalues of the Sturm-Liouville problem. The Sturm-Liouville problem is an infinite dimensional eigenvalue problem that often arises in solving partial differential equations, including the heat and wave equations. To compute eigenvalues of the Sturm-Liouville problem...

In this paper, we present an algorithm for computing the characteristic polynomial of the pencil (A ? sE). It is shown that after a preliminary reduction of the matrices A and E to, respectively, an upper Hessenberg and an upper triangular matrix, the problem of computing the characteristic polynomial is transformed to the solution of certain triangular systems of linear algebraic equations. We...

Each family of Gauss hypergeometric functions fn = 2F1(a + ε1n, b + ε2n; c + ε3n; z), n ∈ Z , for fixed εj = 0,±1 (not all εj equal to zero) satisfies a second order linear difference equation of the form Anfn−1 + Bnfn + Cnfn+1 = 0. Because of symmetry relations and functional relations for the Gauss functions, many of the 26 cases (for different εj values) can be transformed into each other. I...