Quantum Mechanics without an Equation of Motion

Abstract

We propose a formulation of quantum mechanics in three dimensions with spherical symmetry for a finite level system whose dynamics is not governed by a differential equation of motion. The wavefunction is written as an infinite sum in a complete set of square integrable functions. Interaction in the theory is introduced in function space by a real finite tridiagonal symmetric matrix. Information about the structure and dynamics of the system is contained in the scattering matrix, which is defined in the usual way.

7 pages, 2 figures, and 3 tables

References in corpus (5)

• Analytic solution of the Schrodinger equation for an electron in the field of a molecule with an electric dipole moment
• Relativistic scattering with spatially-dependent effective mass in the Dirac equation
• Charged particle in the field an electric quadrupole in two dimensions
• Scattering theory with a natural regularization: Rediscovering the J-matrix method
• Sine function with a cosine attitude