Smoothness and non-smoothness of the fundamental solution of time dependent Schrödinger equations
From MaRDI portal
Publication:679391
DOI10.1007/BF02101289zbMath0883.35022MaRDI QIDQ679391
Publication date: 22 April 1997
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Schrödinger operator, Schrödinger equation (35J10) Fundamental solutions to PDEs and systems of PDEs with constant coefficients (35E05)
Related Items
Smoothness of the fundamental solution of Schrödinger equations with mild trapping, Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity, Probability and Quantum Symmetries. II. The Theorem of Nœther in quantum mechanics, GEOMETRIC APPROACH TO THE HAMILTON–JACOBI EQUATION AND GLOBAL PARAMETRICES FOR THE SCHRÖDINGER PROPAGATOR, The Van Vleck formula on Ehrenfest time scales and stationary phase asymptotics for frequency-dependent phases, Smoothness of solutions for Schrödinger equations with unbounded potentials, An asymptotic functional-integral solution for the Schrödinger equation with polynomial potential, Wave Front Set for Solutions to Perturbed Harmonic Oscillators, Unnamed Item, Commutator algebra and abstract smoothing effect, Propagation of singularities and growth for Schrödinger operators, Global energy solutions to a stochastic Schrödinger-Poisson system with multiplicative noise in two dimensions, SPATIAL GROWTH OF FUNDAMENTAL SOLUTIONS FOR CERTAIN PERTURBATIONS OF THE HARMONIC OSCILLATOR, Sharp weights in the Cauchy problem for nonlinear Schrödinger equations with potential, The semiclassical resolvent and the propagator for non-trapping scattering metrics, LINEAR VS. NONLINEAR EFFECTS FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL, Unitary propagators for N-body Schrödinger equations in external field, Coherent States for Systems ofL2-Supercritical Nonlinear Schrödinger Equations, A fundamental solution to the Schrödinger equation with Doss potentials and its smoothness, Global parametrices for the Schrödinger propagator and geometric approach to the Hamilton-Jacobi equation, Remarks on the fundamental solution to Schrödinger equation with variable coefficients, ON THE BEHAVIOR AT INFINITY OF THE FUNDAMENTAL SOLUTION OF TIME DEPENDENT SCHRÖDINGER EQUATION, Wave front set for solutions to Schrödinger equations with long-range perturbed harmonic oscillators, Semiclassical singularities propagation property for Schrödinger equations, Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation, \(\mathcal H^s\) solutions for nonlinear Schrödinger equations with potentials superquadratic at infinity, Regularity and decay of solutions to the Stark evolution equation, Smoothing estimates for the Schrödinger equation with unbounded potentials, Wave front set of solutions to Schrödinger equations with perturbed harmonic oscillators, SCHRÖDINGER EQUATIONS WITH TIME-DEPENDENT UNBOUNDED SINGULAR POTENTIALS, Boundedness and continuity of the fundamental solution of the time dependent Schrödinger equation with singular potentials, The trace of the generalized harmonic oscillator, FUNCTIONAL-INTEGRAL SOLUTION FOR THE SCHRÖDINGER EQUATION WITH POLYNOMIAL POTENTIAL: A WHITE NOISE APPROACH, Dispersion of singularities of solutions for Schrödinger equations, Feynman path integrals for the inverse quartic oscillator, Propagation of Singularities for Schrödinger Equations on the Euclidean Space with a Scattering Metric, Observable sets, potentials and Schrödinger equations, Singularities for solutions to Schrödinger equations with asymptotically constant magnetic fields
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A construction of the fundamental solution for the Schrödinger equation
- Reconstruction of singularities for solutions of Schrödinger's equation
- Smoothing effects and dispersion of singularities for the Schrödinger evolution group
- Existence of solutions for Schrödinger evolution equations
- Remarks on convergence of the Feynman path integrals
- A family of Fourier integral operators and the fundamental solution for a Schrödinger equation
- Schrödinger evolution equations with magnetic fields
- Propagation des singularités des solutions d'équations pseudo-différentielles quasi homogènes
- Dispersive smoothing for Schrödinger equations
- On Fourier coefficients and transforms of functions of two variables
- Microlocal dispersive smoothing for the Schrödinger equation