FRACTIONAL QUANTUM EULER–CAUCHY EQUATION IN THE SCHRÖDINGER PICTURE, COMPLEXIFIED HARMONIC OSCILLATORS AND EMERGENCE OF COMPLEXIFIED LAGRANGIAN AND HAMILTONIAN DYNAMICS

Abstract

Fractional quantum Euler–Cauchy equation in the Schrödinger picture is derived from the fractional action-like variational approach recently introduced by the author. Many interesting consequences are revealed and explored, in particular the emergence of complexified harmonic oscillators, complexified Lagrangian and Hamiltonian and complexified fractional action integral.