Abstract Using some properties of the Bessel functions the algebraic representation of the Nakajima–Zwanzig generalized master equation was derived. This representation makes possible the calculation of the memory functions in terms of the probabilities. Using this approach, the formulas for the memory functions giving their dependence on the eigenvalues and eigenvectors of the corresponding stationary Schrödinger equation are given and discussed in detail.

International Journal of Quantum ChemistryFeb 1, 19838 citations

3D Schrödinger equation: scattering operator, scattering amplitude and ergodic property

Lev Sakhnovich

arXiv:1905.07608May 18, 20191 citation

Undergraduate lecture notes in physics

Properties of the Stationary Schrödinger Equation

Pedro Pereyra Padilla

Published Jan 1, 2012• 1 citation

Publisher

DOI: 10.1007/978-3-642-29378-8_3

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Lev Sakhnovich

Stationary scattering problem (when the distance $r$ tends to infinity) and dynamical scattering problem (when the time $t$ tends to infinity) are considered for the 3D Schrödinger equation. A simple interconnection between the scattering amplitude (stationary case) and scattering operator (dynamical case) is given in the paper. This result is a quantum mechanical analog of the ergodic formulas in the classical mechanics.Stationary scattering problem (when the distance $r$ tends to infinity) and dynamical scattering problem (when the time $t$ tends to infinity) are considered for the 3D Schrödinger equation. A simple interconnection between the scattering amplitude (stationary case) and scattering operator (dynamical case) is given in the paper. This result is a quantum mechanical analog of the ergodic formulas in the classical mechanics.

arXiv:1905.07608May 18, 20191 citation

Stationary scattering problem (when the distance

r

tends to infinity) and dynamical scattering problem (when the time

t

tends to infinity) are considered for the 3D Schrödinger equation. A simple interconnection between the scattering amplitude (stationary case) and scattering operator (dynamical case) is given in the paper. This result is a quantum mechanical analog of the ergodic formulas in the classical mechanics.