Pendulum View of The Schroedinger Equation
Biao Wu
TL;DR
This paper introduces a transformation linking the one-dimensional Schrödinger equation to a pendulum problem, enabling the construction of exact solutions and relating it to the Zakharov-Shabat equations.
Contribution
It presents a novel transformation between the Schrödinger equation and a pendulum problem, providing a new method for exact solutions and connecting to integrable systems.
Findings
Established a transformation between Schrödinger and pendulum equations
Demonstrated how to construct exact solutions using the pendulum form
Linked the transformation to Zakharov-Shabat equations
Abstract
A transformation is found between the one dimensional Schroedinger equation and a pendulum problem. It is demonstrated how to construct exact solutions with the resulted pendulum equation. The relation of this transformation to the Zakharov-Shabat equations is pointed out.
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Taxonomy
TopicsExperimental and Theoretical Physics Studies · Quantum and Classical Electrodynamics