Rigorous Quantum Mechanics
Self-adjoint operators, spectral theory, and the Schrödinger equation.
Rigorous Quantum Mechanics. Self-adjoint operators, spectral theory, and the Schrödinger equation.
Foundations and canonical references
The standard treatments of rigorous quantum mechanics approach the subject from complementary angles. Reed, Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness (1975) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Neumann, Mathematical Foundations of Quantum Mechanics (1955) provides historical context and an early systematic exposition of the material.
Open methodological questions for rigorous quantum mechanics include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1975Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointnessreed-1975, simon-1975
- textbook · historical · 1955Mathematical Foundations of Quantum Mechanicsvonneumann-1955
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