Symmetry breaking interactions for the time dependent Schrödinger equation

DOI10.1063/1.523068zbMath0326.35019OpenAlexW2019673917MaRDI QIDQ4090748

R. T. Sharp, Charles P. Boyer, Pavel Winternitz

Publication date: 1976

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.523068

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Schrödinger operator, Schrödinger equation (35J10)

Related Items (22)

Symmetry reduction for nonlinear relativistically invariant equations ⋮ Dynamical symmetries of semi-linear Schrödinger and diffusion equations ⋮ Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations ⋮ Symmetry Breaking for Black–Scholes Equations ⋮ An Introduction to Special Functions with Some Applications to Quantum Mechanics ⋮ HIGHEST WEIGHT REPRESENTATIONS AND KAC DETERMINANTS FOR A CLASS OF CONFORMAL GALILEI ALGEBRAS WITH CENTRAL EXTENSION ⋮ Continuous subgroups of the generalized Schrödinger groups ⋮ Subgroups of the Euclidean group and symmetry breaking in nonrelativistic quantum mechanics ⋮ On a hidden symmetry of quantum harmonic oscillators ⋮ Symmetries of the Hamilton–Jacobi equation ⋮ Admissible transformations and normalized classes of nonlinear Schrödinger equations ⋮ Optimal systems and group classification of \((1+2)\)-dimensional heat equation ⋮ Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups ⋮ An ``Airy gun: self-accelerating solutions of the time-dependent Schrödinger equation in vacuum ⋮ The optical group and its subgroups ⋮ Symmetry breaking interactions for the Schrödinger equation in three-dimensional space-time ⋮ Dynamical symmetries of rotationally invariant, three-dimensional, Schrödinger equations ⋮ Evolution equations invariant under two-dimensional space–time Schrödinger group ⋮ Symmetry of time-dependent Schrödinger equations. I. A classification of time-dependent potentials by their maximal kinematical algebras ⋮ Symmetry analysis and conservation laws of the Zoomeron equation ⋮ Subgroups of Lie groups and separation of variables ⋮ Nonlinear action of Lie groups and superposition principles for nonlinear differential equations

Cites Work

• Connected subgroups of the Poincaré group. I
• Irreducible unitary representations of the Lorentz group
• Subgroups of the similitude group of three-dimensional Minkowski space
• The maximal solvable subgroups of the SU(p,q) groups and all subgroups of SU(2,1)
• Lie theory and separation of variables. 6. The equation i U t + Δ2U = 0
• Prolongation structures of nonlinear evolution equations
• The Group $O(4)$, Separation of Variables and the Hydrogen Atom
• Subgroups of the Poincaré group and their invariants
• The Galilei group and its connected subgroups
• Lie Theory and Separation of Variables. I: Parabolic Cylinder Coordinates
• A new basis for the representations of the rotation group. Lamé and Heun polynomials
• Lie theory and separation of variables. 3. The equation ftt−fss =γ2f
• Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0

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