6. Quantization of Linear Differential Equations

Valerij V. Kozlov

Harold V. McIntosh

Dominic William Berry

Jason D. Tran, Leanne Doughty, James K. Freericks

Central force problems involve coupled linear differential equations of motion. By decoupling the differential equations, we show how to efficiently solve for the orbits of the Kepler problem without any complicated integrals. Introducing quantization provides a deep connection between the solution for these classical orbits and the quantum Hamiltonian of hydrogen for states that have definite total angular momentum.

Chihong Chou

Based on a simple observation that a classical second order differential equation may be decomposed into a set of two first order equations, we introduce a Hamiltonian framework to quantize the damped systems. In particular, we analyze the system of a linear damped harmonic oscillator and demonstrate that the time evolution of the Schrödinger equation is unambiguously determined.

Jerome K. Percus