From Kepler to Schrödinger… and Beyond

David B. Cook

Orientation and Outlook Probabilities: Simple Probabilities A More Careful Look at Probabilities Classical Mechanics: The Hamilton-Jacobi Equation Angular Momentum Schrodinger's Mechanics: Prelude: Particle Diffraction The Genesis of Schrodinger's Mechanics The Schrodinger Equation Identities: Momenta and Dynamical Variables Abstracting the Structure Interpretation from Applications: The Quantum Kepler Problem The Harmonic Oscillator and Fields Perturbation Theory and Epicycles Formalisms and Hidden Variables Disputes and Paradoxes: Measurement at the Microscopic Level Paradoxes Beyond Schrodinger's Mechanics?

Omer Faruk Dayi, I. H. Duru

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Kepler and oscillator potentials are q-deformed. The q-canonical transformation connecting two realizations is given and a general definition for the q-canonical transformation is deduced. A q-Schrodinger equation for a Kepler-like potential is obtained from the q-oscillator Schrodinger equation. The energy spectrum and the ground-state wavefunction are calculated.

Willis E. Lamb

Luis de la Peña, Ana Marı́a Cetto, Andrea Valdés Hernández

Omer Faruk Dayi, Ý. H. Duru