Given a particular solution of a one-dimensional stationary Schrödinger equation this equation of second order can be reduced to a first order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or thr...

In this work, we construct the general solution to the Heat Equation (HE) and to many tensor structures associated to the Heat Equation, such as Symmetries, Lagrangians, Poisson Brackets (PB) and Lagrange Brackets (LB), using newly devised techniques that may be applied to any linear equation (e.g., Schrödinger Equation in field theory, or the small-oscillations problem in mechanics). In partic...

The Schrödinger equation for stationary states with non-Fuchsian singularities both at the origin and at infinity can be studied with the help of a suitable change of independent variable, here taken to be of the form ρ = r , where γ is a real parameter greater than 1 and r is the original independent variable. Whenever the potential contains a finite number of negative and positive powers of r...

The wavefunction ψ for a system of N electrons under the time-independent, non-relativistic, multiparticle Schrödinger equation with the Born-Oppenheimer approximation is an antisymmetric function of N variables, each of the form γ = (r, σ) = ((x, y, z), σ) where σ ∈ {−1/2, 1/2} is the spin variable. A natural way to approximate ψ is as the antisymmetrization of a sum of products of functions o...

Trends in the chemical reactivity of transition-metal surfaces have been studied at the example of the dissociative adsorption of hydrogen on the ~100! surfaces of Rh, Pd, and Ag. Detailed calculations of the six-dimensional potential-energy surfaces have been performed using density-functional theory. The adsorption dynamics has been investigated by solving the time-independent Schrödinger equ...

For a time-independent Schrödinger equation with Hamiltonian operator H = −∆ + V on L(R ) we call Gz = RzV , the Green function operator, where Rz is the resolvent of −∆. We consider an iteration scheme that is based on the operator Gz. Under standard conditions on the potential V , which include the Coulomb interaction, we prove the convergence of the iteration to the ground state energy and e...