Mathematical Methods in Quantum Mechanics
by Gerald Teschl
Publisher: American Mathematical Society 2009
Number of pages: 317
This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required.
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by Peter Woit - Columbia University
These notes cover the basics of quantum mechanics, from a point of view emphasizing the role of unitary representations of Lie groups in the foundations of the subject. The approach to this material is simultaneously rather advanced...
by Douglas Lundholm - arXiv.org
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 mathematical methods in many-body quantum mechanics.
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The author reviews the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas ...
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This book is an attempt to help students transform all of the concepts of quantum mechanics into concrete computer representations, which can be analyzed and understood at a deeper level than what is possible with more abstract representations.