# Mathematical Methods in Quantum Mechanics

@inproceedings{Teschl2009MathematicalMI, title={Mathematical Methods in Quantum Mechanics}, author={Gerald Teschl}, year={2009} }

Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction…

## 282 Citations

### Time-Evolution as an Operator in Hilbert Spaces with Applications in Quantum Mechanics

- Physics, Mathematics
- 2014

ABSTRACT: The main aim of this article is to present the time-evolution as the unitary and self-adjoint operators on Hilbert spaces and to describe its application in the development of quantum…

### Spectral and Eigenfunction correlations of finite-volume Schrödinger operators

- Physics, Mathematics
- 2015

The goal of this thesis is a mathematical understanding of a phenomenon called Anderson's Orthogonality in the physics literature. Given two non-interacting fermionic systems which differ by an…

### Fundamental Mathematical Structures of Quantum Theory

- Physics
- 2019

measure theory [Coh80, Rud86], elementary notions of complex Hilbert space theory [Rud86, Mor18], and the basic theory of Fourier(-Plancherel) transform. Some already acquired elementary notions…

### Observables and States in General Hilbert Spaces: Spectral Theory

- MathematicsFundamental Mathematical Structures of Quantum Theory
- 2019

The overall goal of this chapter is to extend the elementary decomposition of a Hermitian operator ( 1.4) on a finite-dimensional Hilbert space seen in Chap. 1 to a formula valid in the…

### Time and the Foundations of Quantum Mechanics

- Philosophy, Physics
- 2014

Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One…

### Self-adjoint operators and solving the Schrödinger equation Basics collected

- Mathematics
- 2014

In this tutorial we collect facts from the theory of self-adjoint operators, mostly with a view of what is relevant for applications in mathematical quantum mechanics, in particular for solving the…

### Methods of modern mathematical physics: Uncertainty and exclusion principles in quantum mechanics

- Physics
- 2018

These are lecture notes for a master-level course given at KTH, Stockholm, in the spring of 2017, with the primary aim of proving the stability of matter from first principles using modern…

### Quantum Zeno Effect in Open Quantum Systems

- Physics, MathematicsAnnales Henri Poincaré
- 2021

We prove the quantum Zeno effect in open quantum systems whose evolution, governed by quantum dynamical semigroups, is repeatedly and frequently interrupted by the action of a quantum operation. For…

## References

SHOWING 1-10 OF 64 REFERENCES

### Advanced visual quantum mechanics

- Physics
- 2005

Advanced Visual Quantum Mechanics is a systematic effort to investigate and to teach quantum mechanics with the aid of computer-generated animations. Although it is self-contained, this book is part…

### Quantum mechanics of atoms and molecules

- Physics
- 1981

The third volume of this textbook on mathematical physics is devoted to quantum mechanics and especially to its applications to atomic systems. The author builds the theory on an axiomatic basis and…

### Non-Relativistic Quantum Dynamics

- Mathematics
- 1981

1: Linear Operators in Hilbert Space.- 1.1 Hilbert Space.- 1.2 Linear Operators.- 1.3 Integration in Hilbert Space.- 2: Self-Adjoint Operators. SchrOEdinger Operators.- 2.1 Self-Adjointness…

### Inverse Problems in Quantum Scattering Theory

- Physics, Mathematics
- 1977

The physical importance of inverse problems in quantum scattering theory is clear since all the information we can obtain on nuclear, particle, and subparticle physics is gathered from scattering…

### Quantum Mechanics for Hamiltonians Defined as Quadratic Forms

- Computer Science
- 1971

This monograph combines a thorough introduction to the mathematical foundations of n-body Schrodinger mechanics with numerous new results to greatly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press.

### Scattering theory of waves and particles

- Physics
- 1966

Much progress has been made in scattering theory since the publication of the first edition of this book fifteen years ago, and it is time to update it. Needless to say, it was impossible to…

### Mathematical scattering theory

- Mathematics
- 1992

The main subject of this book is applications of methods of scattering theory to differential operators, primarily the Schrodinger operator. There are two different trends in scattering theory for…

### Lectures on Quantum Mechanics for Mathematics Students

- Physics
- 2009

This book is based on notes from the course developed and taught for more than 30 years at the Department of Mathematics of Leningrad University. The goal of the course was to present the basics of…

### Hilbert Space Operators in Quantum Physics

- Mathematics
- 1994

Preface to the second edition, Preface,. 1.Some notions from functional analysis,Vector and normed spaces,1.2 Metric and topological spaces,1.3 Compactness, 1.4 Topological vector spaces, 1.5 Banach…

### Visual Quantum Mechanics

- Physics
- 2006

"Visual Quantum Mechanics" is a large collection of Mathematica-generated movies showing quantum-mechanical phenomena. A set of Mathematica packages and associated notebooks help to solve the…