Advanced quantum mechanics : A practical guide / Yuli V Nazarov, Delft University of Technology, Jeroen Danon, Free University of Berlin.

Format:

Book

Author/Creator:

Nazarov, Yuli V., author.

Danon, Jeroen, 1977- author.

Language:

English

Subjects (All):

Quantum theory--Textbooks.

Quantum theory.

Physical Description:

1 online resource (xiv, 354 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2013.

Language Note:

English

Summary:

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.

Contents:

Cover; Contents; Figure Credits; Preface; PART I SECOND QUANTIZATION; 1 Elementary quantum mechanics; 1.1 Classical mechanics; 1.2 Schrödinger equation; 1.3 Dirac formulation; 1.4 Schrödinger and Heisenberg pictures; 1.5 Perturbation theory; 1.6 Time-dependent perturbation theory; 1.6.1 Fermi's golden rule; 1.7 Spin and angular momentum; 1.7.1 Spin in a magnetic field; 1.7.2 Two spins; 1.8 Two-level system: The qubit; 1.9 Harmonic oscillator; 1.10 The density matrix; 1.11 Entanglement; Exercises; Solutions; 2 Identical particles; 2.1 Schrödinger equation for identical particles

2.2 The symmetry postulate2.2.1 Quantum fields; 2.3 Solutions of the N-particle Schrödinger equation; 2.3.1 Symmetric wave function: Bosons; 2.3.2 Antisymmetric wave function: Fermions; 2.3.3 Fock space; Exercises; Solutions; 3 Second quantization; 3.1 Second quantization for bosons; 3.1.1 Commutation relations; 3.1.2 The structure of Fock space; 3.2 Field operators for bosons; 3.2.1 Operators in terms of field operators; 3.2.2 Hamiltonian in terms of field operators; 3.2.3 Field operators in the Heisenberg picture; 3.3 Why second quantization?; 3.4 Second quantization for fermions

3.4.1 Creation and annihilation operators for fermions3.4.2 Field operators; 3.5 Summary of second quantization; Exercises; Solutions; PART II EXAMPLES; 4 Magnetism; 4.1 Non-interacting Fermi gas; 4.2 Magnetic ground state; 4.2.1 Trial wave function; 4.3 Energy; 4.3.1 Kinetic energy; 4.3.2 Potential energy; 4.3.3 Energy balance and phases; 4.4 Broken symmetry; 4.5 Excitations in ferromagnetic metals; 4.5.1 Single-particle excitations; 4.5.2 Electron-hole pairs; 4.5.3 Magnons; 4.5.4 Magnon spectrum; Exercises; Solutions; 5 Superconductivity; 5.1 Attractive interaction and Cooper pairs

5.1.1 Trial wave function5.1.2 Nambu boxes; 5.2 Energy; 5.2.1 Energy minimization; 5.3 Particles and quasiparticles; 5.4 Broken symmetry; Exercises; Solutions; 6 Superfluidity; 6.1 Non-interacting Bose gas; 6.2 Field theory for interacting Bose gas; 6.2.1 Hamiltonian and Heisenberg equation; 6.3 The condensate; 6.3.1 Broken symmetry; 6.4 Excitations as oscillations; 6.4.1 Particles and quasiparticles; 6.5 Topological excitations; 6.5.1 Vortices; 6.5.2 Vortices as quantum states; 6.5.3 Vortex lines; Exercises; Solutions; PART III FIELDS AND RADIATION; 7 Classical fields

7.1 Chain of coupled oscillators7.2 Continuous elastic string; 7.2.1 Hamiltonian and equation of motion; 7.2.2 Solution of the equation of motion; 7.2.3 The elastic string as a set of oscillators; 7.3 Classical electromagnetic field; 7.3.1 Maxwell equations; 7.3.2 Useful relations; 7.3.3 Vector and scalar potentials; 7.3.4 Gauges; 7.3.5 Electromagnetic field as a set of oscillators; 7.3.6 The LC-oscillator; Exercises; Solutions; 8 Quantization of fields; 8.1 Quantization of the mechanical oscillator; 8.1.1 Oscillator and oscillators; 8.2 The elastic string: phonons

8.3 Fluctuations of magnetization: magnons

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

ISBN:

1-107-23317-8

1-139-60972-6

1-107-25353-5

1-139-61158-5

1-139-62088-6

1-283-97025-2

1-139-62460-1

1-139-61530-0

0-511-98042-6

OCLC:

827212246