Lectures on QM for mathematicians conjecture that quantum transitions and duality emerge from attractors in nonlinear Hamiltonian PDEs, supported by model cases since 1990 but open for Maxwell-Schrödinger, plus Kirchhoff-approximation calculations for diffraction and Aharonov-Bohm shift.
Solitary waves for Maxwell-Schrodinger equations
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abstract
In this paper we study the solitary waves for the coupled Schr\"odinger - Maxwell equations in three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed $L^2$ norm. We study the asymptotic behavior and the smoothness of these solutions. We show also the fact that the eigenvalues are negative and the first one is isolated.
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2019 1verdicts
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Lectures on Quantum Mechanics for mathematicians
Lectures on QM for mathematicians conjecture that quantum transitions and duality emerge from attractors in nonlinear Hamiltonian PDEs, supported by model cases since 1990 but open for Maxwell-Schrödinger, plus Kirchhoff-approximation calculations for diffraction and Aharonov-Bohm shift.