By Dirk Dubbers

This concise educational presents the bachelor pupil and the practitioner with a quick textual content on quantum physics that permits them to appreciate a wealth of quantum phenomena in accordance with a compact, good readable, but nonetheless concise and actual description of nonrelativistic quantum concept. This “quadrature of the circle” is completed by means of concentrating first at the easiest quantum procedure that also monitors all uncomplicated positive aspects of quantum idea, specifically, a process with merely quantized strength degrees. for many readers it's very beneficial to appreciate such basic platforms prior to slowly continuing to extra not easy themes like particle entanglement, quantum chaos, or using irreducible tensors. This educational doesn't intend to switch the normal textbooks on quantum mechanics, yet can help the typical scholar to appreciate them, frequently for the 1st time.

Table of Contents

Cover

Quantum Physics: The Bottom-Up method - From the easy Two-Level process to Irreducible Representations

ISBN 9783642310591 ISBN 9783642310607

Preface

Contents

Part I Prologue

bankruptcy 1 reminiscences from hassle-free Quantum Physics

Part II Two-State Quantum Systems

bankruptcy 2 A most basic Two-Level System

2.1 Magnetic second and Spin

2.2 Zeeman Effect

2.3 Stern-Gerlach Effect

bankruptcy three Quantum concept in a Nutshell

3.1 Spin Matrices

3.2 power Matrices

3.3 Expectation Values

o 3.3.1 Expectation price of Energy

o 3.3.2 Expectation worth of Spin

3.4 Uncertainties

o 3.4.1 Uncertainty of Spin

o 3.4.2 Uncertainty of Energy

3.5 Spin Precession

o 3.5.1 Longitudinal Field

o 3.5.2 Transverse Field

bankruptcy four Experiments on Spin Precession

4.1 Muon Spin Precession

4.2 gentle Scattering

4.3 Spinor Rotation via 720�

bankruptcy five normal answer for the Two-Level System

5.1 Matrix Diagonalization

5.2 development of the Eigenvectors

5.3 The Time based Solution

o 5.3.1 Evolution of an strength Eigenstate

o 5.3.2 Evolution of an Angular-Momentum Eigenstate

bankruptcy 6 different instruments and Concepts

6.1 Time Evolution Operator

6.2 Rotation Matrices

6.3 Projection Operators

6.4 natural States and combined States

6.5 The Density Matrix

6.6 Coherence and Interference

6.7 Dirac's Bra-Ket Notation

bankruptcy 7 Diabolic issues, Geometric levels, and Quantum Chaos

7.1 point Crossings and point Repulsions

o 7.1.1 the sector Dependence of strength and of Polarization

o 7.1.2 point Repulsion in a Spin1

o 7.1.3 point Repulsion in a Spin-1 System

7.2 The Adiabatic Theorem

7.3 Geometric Phases

o 7.3.1 Derivation of the Berry Phase

o 7.3.2 tours in Magnetic-Field Space

o 7.3.3 tours within the area of Shapes

o 7.3.4 The Aharonov-Bohm Effect

7.4 Quantum Chaos

bankruptcy eight The Coupling of Particles

8.1 Bosons and Fermions

8.2 The Coupling of Spins

8.3 instance: Hyperfin Structure

bankruptcy nine "Spooky motion at a Distance"

9.1 Quantum Entanglement

9.2 Bell's Inequalities

bankruptcy 10 The Heisenberg Equation of Motion

10.1 Matrix Mechanics

10.2 Commutation relatives and Uncertainty Principle

10.3 The Bloch Equations

Part III Quantum Physics at Work

bankruptcy eleven Spin Resonance

11.1 fundamentals of Spin Resonance

11.2 tools of Spin Resonance

11.3 functions of Spin Resonance

bankruptcy 12 Two-State platforms in Atomic and Molecular Physics

12.1 Photons as Two-State Systems

12.2 Optical Resonance Transitions

12.3 Optical Analogies of Spin Rotation and Spin Resonance

12.4 debris in a Double Well

o 12.4.1 The NH3 Molecule

o 12.4.2 The Ammonia Maser

o 12.4.3 Bose-Einstein Condensate in a Double Trap

bankruptcy thirteen Two-State platforms in Condensed Matter

13.1 Glasses

13.2 Josephson Effects

o 13.2.1 fundamentals of Superconductivity

o 13.2.2 Josephson Junctions and Their Applications

bankruptcy 14 Two-State platforms in Nuclear and Particle Physics

14.1 Isospin

14.2 taste and Color

14.3 Particle Oscillations

o 14.3.1 Kaon Oscillations

o 14.3.2 Neutrino Oscillations

o 14.3.3 Neutron Oscillations

bankruptcy 15 Quantum Informatics

15.1 Quantum details Theory

15.2 Quantum Computing and Quantum Communication

Part IV Multilevel platforms and Tensor Operators

bankruptcy sixteen Rotations and Angular Momentum

16.1 Symmetries

16.2 homes of Angular Momentum

16.3 Representations

16.4 The round Harmonics

16.5 The Rotation Matrices

bankruptcy 17 Irreducible Tensors

17.1 Scalars, Vectors, and Tensors

17.2 houses of Irreducible Tensors

o 17.2.1 Definition of Irreducible Tensors

o 17.2.2 A simpler Definitio

o 17.2.3 easy Examples

17.3 The Coupling of Irreducible Tensors

o 17.3.1 The Coupling of Angular Momenta

o 17.3.2 basic Tensor Coupling

o 17.3.3 a few detailed Cases

17.4 The Wigner-Eckart Theorem

bankruptcy 18 Electromagnetic Multipole Interactions

18.1 Static Magnetic Interactions

18.2 Static electrical Interactions

o 18.2.1 Multipole growth of Electrostatic Energy

o 18.2.2 electrical Quadrupole Interaction

18.3 choice ideas for Electromagnetic Transitions

bankruptcy 19 The Generalized Spin Precession Equation

19.1 The Density Matrix

o 19.1.1 Definition of the Density Matrix

o 19.1.2 The Liouville Equation of Motion

19.2 a few Preparative Steps

o 19.2.1 Normalized Irreducible Tensor Operators

o 19.2.2 A Bra-Ket Notation for Tensor Operators

19.3 The Irreducible elements of the Density Matrix

o 19.3.1 Definition of the Statistical Tensors

o 19.3.2 basic Examples of Statistical Tensors

19.4 The Liouville Equation for the Statistical Tensors

bankruptcy 20 Reorientation in Static Electromagnetic Fields

20.1 Magnetic Dipole Precession

20.2 electrical Quadrupole Reorientation

20.3 Reorientation in combined Magnetic and electrical Fields

20.4 Time typical Results

20.5 Angular Distribution of Radiation

o 20.5.1 uneven �-Decay

o 20.5.2 Anisotropic Photon Emission

bankruptcy 21 Reorientation in Time established Fields

21.1 Radiofrequency Irradiation in a Magnetic Field

o 21.1.1 Density Operator within the Rotating Frame

o 21.1.2 Rotating Wave Approximation

o 21.1.3 Statistical Tensors within the Rotating Wave Approximation

o 21.1.4 Time commonplace Results

21.2 a number of Quantum Transitions

21.3 Dressed Atoms

o 21.3.1 Dressed Atoms and the Floquet Theorem

o 21.3.2 Dressed Atoms and moment Quantization

o 21.3.3 A Dressed Neutron Experiment

o 21.3.4 Outlook on Nonclassical Photon Interactions

bankruptcy 22 rest and Decoherence

22.1 normal Features

22.2 The Perturbative Approach

22.3 The Stochastic Approach

22.4 Decoherence

Appendices

Index