This textbook has the following four prominent features: 1. To teach advanced quantum mechanics more clearly and simply. 2. To give some new applications which the quantum mechanics cannot give due to its limitations in methods. 3. To eliminate some mistakes in both physical concepts and pure mathematics. 4. To shorten the distance between study and research. Even you are a student or a beginner, you already can write high quality papers, and can bring forth new ideas in new technology. It might be that no one reader believes this. Rather than the ordinary axiomatic approach to establish quantum mechanics upon postulates, in "Quantum Mechanics upon Theorems", the author of this textbook proved 52 theorems, 16 corollaries, one criterion, and establishes one law. Advanced quantum mechanics is the natural extension of quantum mechanics upon theorems. To make advanced quantum mechanics clear and simple, this textbook introduces the theorems, corollaries, criterion, and law of "Quantum Mechanics upon Theorems" in Chapter 1. In the other 9 chapters, this textbook proves 20 new theorems and 7 new corollaries.
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