Non-Hermitian Wave Mechanics: An Unorthodox Way into Embedded Systems

Abstract

where m is the mass of a particle which moves under the influence of a real potential V(r) (ħ is the reduced Planck constant h/2π). When V(r) does not depend on time t the eigenvalues En of the Hermitian Hamiltonian H are the energy levels of a system. (d) The time evolution of the wave function is given by the timedependent Schrödinger equation Introduction In 1926, Erwin Schrödinger formulated his famous non-relativistic equation for matter waves. In this form quantum mechanics (QM) has since then remained a never-ending success. It expands the classical Newtonian mechanics for particle orbitals into the world of quantum matter as atoms, molecules, solid matter, microand nano-scale devices, etc., in which particles acquire wave properties. For this reason it is also referred to, particularly in the early years of the new theory, as wave mechanics (WM) with reference to common wave phenomena present in acoustics, electromagnetism, vibrational structures as membranes and drums, hydrodynamics and more. The predictive power of QM is, as well known, overwhelming. In short, traditional QM as above rests solidly on a number of postulates as (Schiff, 1968):