Tosio Kato’s work on non-relativistic quantum mechanics: part 1
@article{Simon2017TosioKW, title={Tosio Kato’s work on non-relativistic quantum mechanics: part 1}, author={Barry Simon}, journal={Bulletin of Mathematical Sciences}, year={2017}, volume={8}, pages={121-232} }
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 in this first part include analytic and asymptotic eigenvalue perturbation theory, Temple–Kato inequality, self-adjointness results, and quadratic forms including monotone convergence theorems.
21 Citations
Differential equations of quantum mechanics
- Physics, MathematicsQuarterly of Applied Mathematics
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We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems.
The Feshbach–Schur map and perturbation theory
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This paper deals with perturbation theory for discrete spectra of linear operators. To simplify exposition we consider here self-adjoint operators. This theory is based on the Feshbach-Schur map and…
Representation of non-semibounded quadratic forms and orthogonal additivity
- MathematicsJournal of Mathematical Analysis and Applications
- 2018
Self-adjointness of non-semibounded covariant Schr\"odinger operators on Riemannian manifolds
- Mathematics
- 2021
In the context of a geodesically complete Riemannian manifold M , we study the self-adjointness of ∇∇+V where ∇ is a metric covariant derivative (with formal adjoint ∇) on a Hermitian vector bundle V…
Twelve tales in mathematical physics: An expanded Heineman prize lecture
- PhysicsJournal of Mathematical Physics
- 2022
This is an extended version of my 2018 Heineman prize lecture describing the work for which I got the prize. The citation is very broad, so this describes virtually all my work prior to 1995 and some…
Spectral triples, Coulhon-Varopoulos dimension and heat kernel estimates
- Mathematics
- 2022
We connect the (completely bounded) local Coulhon-Varopoulos dimension to the spectral dimension of spectral triples associated to sub-Markovian semigroups (or Dirichlet forms) acting on classical…
Quantum theory and functional analysis
- Physics
- 2019
Quantum theory and functional analysis were created and put into essentially their final form during similar periods ending around 1930. Each was also a key outcome of the major revolutions that both…
Sharp bound for embedded eigenvalues of Dirac operators with decaying potentials
- Mathematics
- 2022
. We study eigenvalues of the Dirac operator with canonical form where 𝑝 and 𝑞 are real functions. Under the assumption that the essential spectrum of 𝐿 𝑝,𝑞 is (−∞,∞) . We prove that 𝐿 𝑝,𝑞…
Extensions of symmetric operators that are invariant under scaling and applications to indicial operators
- Mathematics
- 2021
Indicial operators are model operators associated to an elliptic di erential operator near a corner singularity on a strati ed manifold. These model operators are de ned on generalized tangent cone…
UNBOUNDED EIGENVALUE PROBLEMS IN THE GENERALIZED FORM
- Mathematics
- 2019
Unbounded eigenvalue problems in the generalized form are reformulated, implicitly leading to bounded standard eigenvalue problems. By performing implicit linear fractional transformations, the way…
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