Meromorphic Behavior of Time Dependent Schroedinger Equation

Abstract

We try to obtain meromorphic solution of Time dependent Schroedinger equation which partially satisfies Painleve Integrable property. Our study and analysis exhibits meromorphic behavior of classical particle trajectory. In other words, particle is confined in punctured complex domain in singular fundamental domain. . We have explicitly developed solution from Jacobi Elliptic function and pole expansion approach in which solution remains meromorphic . Branch point analysis also shows solution branches out near such singular point. Meromorphic behavior is significant for a classical particle within quantum limit.

arXiv commentKey word: movable singularity, Non Linear ODE, Meromorphic solution

References in corpus (9)

• From Laurent Series to Exact Meromorphic Solutions: the Kawahara equation
• Quantum geometry of 2d gravity coupled to unitary matter
• Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian
• Simulations of Dynamically Triangulated Gravity -- an Algorithm for Arbitrary Dimension
• Two Ising Models Coupled to 2-Dimensional Gravity
• Dynamical Triangulations, a Gateway to Quantum Gravity ?
• A geometric approach to free variable loop equations in discretized theories of 2D gravity
• The Ising model with a boundary magnetic field on a random surface
• Boundary fields and renormalization group flow in the two-matrix model