Advanced Teacher Training in Operator Methods in Quantum Mechanics

Teacher: Dr. Horst R. Beyer.

Date and Time

October 17 – December 8, 2017.
Tuesday and Thursday from 4:00 pm. to 6:00 p.m.

Venue

Sala de Usos Múltiples del MCTP,
Ciudad Universitaria UNACH, Carretera Emiliano Zapata Km. 8, Real del Bosque (Terán).
Tuxtla Gutiérrez, Chiapas, México.

Sponsors

MCTP, CONACYT and UNACH .

Organizers

Horst R Beyer.
Maricela Hernández Arroyo.

Summary

The schedule will be extended in some days in order to complete 40 hours. For students coming form outside Tuxtla, a tutorial plan will be implemented in order to complete 320 hours of work. The plan of work will include homework on mathematics and close collaboration with the teacher in tasks related to the course. This extended schedule will allow UNACH to offer a Diploma with curricular validity.

In addition to abundant experimental evidence, quantum theory has a firm mathematical foundation, provided by the spectral theorems for (densely-defined, linear and) self-adjoint operators in Hilbert Spaces, called “observables” in quantum theory. In particular, these theorems provide the existence of spectral measures associated to self-adjoint operators and elements of the Hilbert space, the latter called “states” in quantum theory. Such spectral measures are the primary observables in quantum theory. One well-known example in one space dimension is the absolute square of the wave-function in quantum mechanics, which generates the spectral measure corresponding to the position operator and that wave function.

Unfortunately, these mathematical facts are not widely known neither inside the mathematics nor the physics community and deserve a lot more distribution, since providing an additional firm foundation of quantum theory, turning it into a “mathematical theory.”

This short course introduces into basic aspects of applications of operator theory to quantum mechanics. It follows to a large extent Martin Schechter's book “Operator Methods in Quantum Mechanics," Dover 2003. “This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus."

Contents
  1. A brief Sketch of the Mathematical Structure of Quantum Theory
  2. Introduction to Banach and Hilbert Spaces
  3. Representation of Formal Differential Operators
  4. Linear Operators in Banach Spaces
  5. Definition and Properties of the Fourier Transform
  6. Spectra of Operators
  7. The Essential Spectrum
  8. One-Dimensional Motion
  9. The Negative Eigenvalues
  10. Estimating the Spectrum
  11. Scattering Theory
  12. Long-Range Potentials
  13. Time-Independent Theory
  14. Completeness
  15. Strong Completeness
  16. Oscillating Potentials
  17. Eigenfunction Expansions
  18. Restricted Particles
  19. Hard-Core Potentials
  20. The Invariance Principle
  21. Trace Class Operators
Registration

https://goo.gl/Hv9hkD

Bulletin

https://goo.gl/iKAZsG
UNACH/MCTP, Ciudad Universitaria
Carretera Emiliano Zapata Km. 4,
Real del Bosque (Terán).
Tuxtla Gutiérrez, Chiapas, México.
C. P. 29050
Teléfono 52 (961) 617-80-00
Ext. 8200 y 1380
mctp@unach.mx
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Desarrollado por MCTP