# Meromorphic Behavior of Time Dependent Schroedinger Equation

@inproceedings{Dutta2021MeromorphicBO, title={Meromorphic Behavior of Time Dependent Schroedinger Equation}, author={Rina Dutta and Adrian Daniel Stan}, year={2021} }

We try to obtain meromorphic solution of Time dependent second Schröedinger equation which partially satisfy Painleve Integrable property. Meromorphic analysis shows that classical particle trajectory is confined in imaginary axis of punctured Riemann disk on singular manifold in quantum limit. The trajectory solution is holomorphic near such singularity and very different from behavior far away from singular point. We have explicitly given value of all coefficients in meromorphic series…

## References

SHOWING 1-10 OF 34 REFERENCES

Exact solutions for time-dependent phenomena in quantum mechanics

- Physics
- 1994

Abstract We review and discuss exact solutions for selected initial value problems. Starting with simple oscillator problems (forced harmonic oscillator, tunneling through a parabolic barrier,…

The singular manifold method revisited

- Mathematics
- 1996

For many completely integrable partial differential equations (PDEs) the singular manifold method of Weiss allows the recovery of the Lax pair and Darboux transformation (DT), and so also the…

Analytic and asymptotic methods for nonlinear singularity analysis: a review and extensions of tests for the Painlevé property

- Mathematics, Physics
- 1997

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is…

From Laurent series to exact meromorphic solutions: The Kawahara equation

- Physics
- 2010

Meromorphic traveling wave solutions of the Kawahara equation and the modified Kawahara equations are studied. An algorithm for constructing meromorphic solutions in explicit form is described. The…

Singularity methods for meromorphic solutions of differential equations

- Mathematics, Physics
- 2018

This chapter is mainly a tutorial introduction to methods recently developed in order to find all (as opposed to some) meromorphic particular solutions of given nonintegrable, autonomous, algebraic…

Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

- Physics
- 2015

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics.…

Necessary condition for the existence of algebraic first integrals

- Physics
- 1983

Existence of algebraic first integrals for a class of dynamical systems is discussed in connection with the nature of the singularities of solutions. It is shown that under some conditions, the…

An Exact Quantum Theory of the Time‐Dependent Harmonic Oscillator and of a Charged Particle in a Time‐Dependent Electromagnetic Field

- Physics
- 1969

The theory of explicitly time‐dependent invariants is developed for quantum systems whose Hamiltonians are explicitly time dependent. The central feature of the discussion is the derivation of a…

Decoherence and the Appearance of a Classical World in Quantum Theory

- Physics
- 1996

1 Introduction.- 2 Basic Concepts and Their Interpretation.- 3 Decoherence Through Interaction with the Environment.- 4 Decoherence in Quantum Field Theory and Quantum Gravity.- 5 Consistent…

The Ermakov equation: A commentary

- Mathematics
- 2008

We present a short history of the Ermakov equation with an emphasis on its discovery by thewest and the subsequent boost to research into invariants for nonlinear systems although recognizing some of…