The Schrdinger equation is fundamentally nonlinear.
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Standard quantum mechanics and the Schrödinger equation are fundamentally linear, with nonlinear variants appearing only as effective descriptions for specific physical systems rather than as a fundamental property.
Erwin Rudolf Josef Alexander Schrödinger (12 August 1887 – 4 January 1961), sometimes anglicised as Schroedinger or Schrodinger, was an Austrian theoretical physicist who developed fundamental results in quantum theory. In particular, he is recognized for devising the Schrödinger equation, an equation that provides a way to calculate the wave function of a system and how it changes dynamically in
Erwin Rudolf Josef Alexander Schrödinger (12 August 1887 – 4 January 1961), sometimes anglicised as Schroedinger or Schrodinger, was an Austrian theoretical physicist who developed fundamental results in quantum theory. In particular, he is recognized for devising the Schrödinger equation, an equation that provides a way to calculate the wave function of a system and how it…
In 1956, following the neutralization of Austria in 1955, Schrödinger returned to Vienna to become a professor emeritus at the University of Vienna. At an important lecture during the World Power Conference, Schrödinger refused to speak on nuclear power because of his scepticism about it and gave a philosophical lecture instead. During this period, he turned from mainstream quantum mechanics' definition of wave–particle duality and promoted the wave idea alone, causing much controversy.
Schrödinger suffered from tuberculosis and several times in the 1920s stayed at a sanatorium in Arosa, Switzerland. It was there that he formulated his wave equation. Schrödinger died of tuberculosis on 4 January 1961 in Vienna at the age of 73. Although not Catholic, he was buried in a Catholic cemetery in Alpbach, after the priest in charge of the cemetery learnt Schrödinger was a Member of the Pontifical Academy of Sciences.
There…
The philosophical issues raised by Schrödinger's cat are still debated today and remain his most enduring legacy in popular science, while Schrödinger's equation is his most enduring legacy at a more technical level. Schrödinger is one of several individuals who have been called "the father of quantum mechanics". Schrödinger crater, on the far side of the Moon, is named after him. The Erwin Schrödinger International Institute for Mathematical Physics was founded in Vienna in 1992.
Schrödinger's portrait was the main feature of the design of the 1983–97 Austrian 1000-schilling banknote, the second-highest denomination. A building is named after him at the University of Limerick in Ireland, as is the Erwin Schrödinger Zentrum in Adlershof, Berlin and the Route Schrödinger at CERN, Prévessin, France. Schrödinger's 126th birthday anniversary in 2013 was celebrated with a Google Doodle.
We present a theoretical technique for solving the quantum transport problem of a few photons through a one-dimensional, strongly nonlinear waveguide. We specifically consider the situation where the evolution of the optical field is governed by the quantum nonlinear Schrödinger equation. Although this kind of nonlinearity is quite general, we focus on a realistic implementation involving cold atoms loaded in a hollow-core optical fiber, where the atomic system provides a tunable nonlinearity that can be large even at a single-photon level. In particular, we show that when the interaction betw
quantum mechanics - Could the Schrödinger equation be nonlinear? - Physics Stack Exchange
# Could the Schrödinger equation be nonlinear?
Asked 14 years, 6 months ago
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Is there any specific reasons why so few consider the possibility that there might be something underlying the Schrödinger equation which is nonlinear? For instance, can't quantum gravity(QG) be nonlinear like general relativity(GR)?
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edited Sep 1, 2014 at 23:24
Qmechanic♦
asked Sep 6, 2011 at 23:41
SchroedingersGhost
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There are nonlinear versions of the Schrodinger equation that are completely irrelevant to your question. These are like the Gross-Pitaevski equation, they are nonlinear classical field equations that describe the flow of a self-interacting superfluid or BEC. These equations have nothing to do with the evolution of probability amplitudes, and I wil
Quantum Theory from a Nonlinear Perspective: Riccati Equations in Fundamental Physics | Springer Nature Link
## Overview
Authors:
- Dieter Schuch 0
Dieter Schuch
Institut für Theoretische Physik, Goethe-University Frankfurt am Main, Frankfurt am Main, Germany
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- A unique survey of the power of Riccati equations to describe reversible and irreversible processes in many areas of physics
- Particular attention paid to non-linear versions of the Schrödinger equation
- Reveals parallels in many seeming unrelated areas of physics, from quantum physics to fluid mechanics and cosmology
- Author is a foremost expert with many years of experience in the field
Part of the book series: Fundamental Theories of Physics(FTPH, volume 191)
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## About this book
This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to clas
Schrödinger equation revisited | PNAS
Contents
## Abstract
The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance, its origin is still not widely appreciated and properly understood. We obtain the Schrödinger equation from a mathematical identity by a slight generalization of the formulation of classical statistical mechanics based on the Hamilton–Jacobi equation. This approach brings out most clearly the fact that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave.
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## Acknowledgments
We thank L. Cohen, J. P. Dahl, J. Dalibard, W. D. Deering, M. Fleischhauer, R. F. O’Connell, H. Paul, E. Sadurni, A. A. Svidzinsky, and W. H. Zurek for many fruitful discussions. D.M.G. is grateful to the Alexander von Humboldt Stiftung which made this project possible. M.O.S. acknowledges the support of the National Science Foundation (Grant PHY-1241032) and the Robert A Welch Foundation (Award A-1261).
## References
1
D Bohm Quantum Theory (Dover, New York, 1989).
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