Tosio Kato's Work on Non--Relativistic Quantum Mechanics
arXiv:1711.00528
Abstract
We review the work of Tosio Kato on the mathematics of non--relativistic quantum mechanics and some of the research that was motivated by this. Topics include analytic and asymptotic eigenvalue perturbation theory, Temple--Kato inequality, self--adjointness results, quadratic forms including monotone convergence theorems, absence of embedded eigenvalues, trace class scattering, Kato smoothness, the quantum adiabatic theorem and Kato's ultimate Trotter Product Formula.
arXiv commentThis is intended for Bull. Math. Sci. which intends to split it in two parts
References in corpus (8)
- Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
- Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators
- Eigenvalue bounds for Schrödinger operators with complex potentials
- General Adiabatic Evolution with a Gap Condition
- The electron density is smooth away from the nuclei
- Mean-field limit of Bose systems: rigorous results
- Bound States at Threshold resulting from Coulomb Repulsion
- Hardy inequalities, Rellich inequalities and local Dirichlet forms
Cited by in corpus (7)
- Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation
- Criteria for embedded eigenvalues for discrete Schrödinger operators
- Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators
- Growth of the eigensolutions of Laplacians on Riemannian manifolds I: construction of energy function
- Tosio Kato's Work on Non-Relativistic Quantum Mechanics: An Outline
- On the domain of a magnetic Schrödinger operator with complex electric potential
- Sharp bound on the largest positive eigenvalue for one-dimensional Schrödinger operators