Advanced Quantum Mechanics

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Product Description

An accessible introduction to advanced quantum theory, this graduate-level textbook focuses on its practical applications rather than mathematical technicalities. It treats real-life examples, from topics ranging from quantum transport to nanotechnology, to equip students with a toolbox of theoretical techniques. Beginning with second quantization, the authors illustrate its use with different condensed matter physics examples. They then explain how to quantize classical fields, with a focus on the electromagnetic field, taking students from Maxwell's equations to photons, coherent states and absorption and emission of photons. Following this is a unique master-level presentation on dissipative quantum mechanics, before the textbook concludes with a short introduction to relativistic quantum mechanics, covering the Dirac equation and a relativistic second quantization formalism. The textbook includes 70 end-of-chapter problems. Solutions to some problems are given at the end of the chapter and full solutions to all problems are available for instructors at www.cambridge.org/9780521761505.

Advanced Quantum Mechanics Review

This is a book can make you smart in Field theory. But it is still good to put it together with "Lectures on Quantum Field Theory"(by Ashok Das). It just reminds me another equally good book "Ultracold Quantum Fields" (Henk T. C. Stoof, Dennis B. M. Dickerscheid, Koos Gubbels).

Harmonic Oscillators are stressed all over the book. It just remind people the importance of Cartan-Weyl representation theory should be acknowledged.

Several Things need to be figured out by a serious physics student:

a) What is perturbation in QM and QFT? How does it relate with representation theories (including SU(2), Cartan-Weyl representation)? Pauli Matrix (Spin 1/2 perturbation case) could naturally be related to SU(2), and spin 1/2 could be the foundation of higher spin perturbation construction (Cartan-Weyl Subgroup). Is there any relation with approximation theory or image processing or digital signal processing? Could wavelet be used in Perturbative Field Theory?

b) What is quantization? What could be obtained classically (without incorporating canonical/path integral quantization rules)? To analyze the "equipotential-line in Phase Space" , before and after the quantization, the insight could be gained from simple examples in Quantum Mechanics. In Heisenberg Equation, unitary operator (which guarantee the conservation of probability -> Liouville Equation in Phase Space, Perfect/Ideal Fluid Model) links the initial state and final state (OR input state and output state in Field Theory). Green's Function could be adopted to mediate the input state and output state, revealing the interaction processes, which has been visualized as Feynmann Diagrams. That higher rank Green's Function could be decoupled into two-point Green's Function, which not merely a technique simplifying the calculation, could correspond to the physical fact that multiple-input, multiple-output interactions could be decoupled to simple interactions like pair creation and annihilation. Further, in the tangent space, the eigenbasis of Hermitian Operator (which could be exponentialized to be unitary operator) decomposes the field quantity and relates it with ladder operators (Cartan-Weyl representation of Lie Group).

c) Two kinds of representation theory. One corresponds to classification of particles and could lead to spin-statistic relation, which further leads to commutators and anti-commutators. Then through complexification and (de-)composition, it could lead to SU(2) Cartan-Weyl representation.

d) SUSY and Conformal Field Theory. ladder operators are hither and thither. But who is whose ladder operator? Is there any mixture?

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