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Hilbert space methods for quantum mechanics
Serge RICHARD Professor
Department: Graduate School of Mathematics
Class Time:  2016 Spring Wednesday 
Recommended for:  Graduate school of Mathematics 
Course Overview
Course Overview
This course will provide an overview of some classical tools of functional analysis which have been partially developed for quantum mechanics. In particular, an introduction to spectral and scattering theory will be presented. These theories have deep connection with other branches of mathematics, like PDE, operator algebras or dynamical systems. Some uptodate tools of spectral theory will also be introduced, as for example commutator methods for spectral theory. In order to provide a large panorama on the subject together with applications, some details might be omitted, but references for all proofs will be provided.
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Syllabus
References
The two main references for this course will be
 Amrein: Hilbert space methods in quantum mechanics, 2009
 Teschl: Mathematical methods in quantum mechanics, 2009
Plan of the course
Tentative program:
 Hilbert space and bounded operators,
 Unbounded operators,
 Selfadjoint operators and spectral theory,
 Some examples,
 Evolution group and scattering theory,
 Commutator methods.
Keywords
Hilbert space, selfadjoint operators, spectral and scattering theory, commutator methods.
Required Knowledge
Knowledge on standard undergraduate functional analysis.
Attendance
This course is open for any students at Nagoya University as one of the “open subjects” of general education.
Method of Evaluation
Grades based on attendance, a written report, or an examination.
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Class Materials
Lecture Notes
 full document (100 pages)
 Hilbert space methods for quantum mechanics (PDF, 404KB)
Lecture Notes
 Title (PDF, 17KB)
 Contents (PDF, 40KB)
 Chapter 1
 Hilbert space and bounded linear operators (PDF, 121KB)
 Chapter 2
 Unbounded operators (PDF, 109KB)
 Chapter 3
 Examples (PDF, 128KB)
 Chapter 4
 Spectral theory for selfadjoint operators (PDF, 141KB)
 Chapter 5
 Scattering theory (PDF, 140KB)
 Chapter 6
 Commutator methods (PDF, 180KB)
 Bibliography
 Bibliography (PDF, 56KB)
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Page last updated September 6, 2016
The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.