Quantum Mechanics

Axiomatic Approach and Understanding Through Mathematics
2023
ISBN: 978-981-99-0493-8
Verlag: Springer Nature Singapore

Buch, Englisch, 314 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 664 g

Reihe: UNITEXT for Physics

This book provides a clear understanding of quantum mechanics (QM) by developing it from fundamental postulates in an axiomatic manner, as its central theme. The target audience is physics students at master’s level. It avoids historical developments, which are piecemeal, not logically well knitted, and may lead to misconceptions. Instead, in the present approach all of QM and all its rules are developed logically starting from the fundamental postulates only and no other assumptions.
Specially noteworthy topics have been developed in a smooth contiguous fashion following the central theme. They provide a new approach to understanding QM. In most other texts, these are presented as disjoint separate topics. Since the reader may not be acquainted with advanced mathematical topics like linear vector space, a number of such topics have been presented as “mathematical preliminary.” Standard topics, viz. derivation of uncertainty relations, simple harmonic oscillator by operator method,bound systems in one and three dimensions, angular momentum, hydrogen-like atom, and scattering in one and three dimensions, are woven into the central theme.
Advanced topics like approximation methods, spin and generalized angular momenta, addition of angular momenta, and relativistic quantum mechanics have been reserved for Volume II.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Das, Tapan Kumar

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

1. Introduction.- 2. Mathematical preliminary I.- 3. Axiomatic approach to Quantum Mechanics.- 4. Formulation of Quantum Mechanics.- 5. General uncertainty relation.- 6. Harmonic oscillator: operator method.- 7. Mathematical preliminary II.- 8. Solution of Schrodinger equation.- 9. One-dimensional potentials.- 10. Three dimensional problem.- 11. Hydrogen-type atoms.- 12. Particle in a 3-D well.- 13. Scattering in 1-dimension.- 14. Scattering in 3-dimension.

Über Autor(innen)

After finishing his M.Sc. from the University of Calcutta (India) in 1965, Prof. Tapan Kumar Das received his Ph.D. in 1971 from the University of Pennsylvania (Philadelphia, USA). He then did his post-doctoral research at the Technische Universität München (Munich, Germany) for a year, before joining (on invitation) the Universidade Federal de Pernambuco (Recife, Brazil) in 1973 as Professor Titular. He taught mathematical methods, quantum mechanics, and nuclear physics to graduate students, besides doing research in nuclear physics and few-body systems. In 1977, he joined the University of Burdwan (WB, India).