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Topics discussed in this pdf include: Introduction, Non-Technical Overview, Mathematical Background, The Foundations of Quantum Theory, Continuous Quantum Systems, The Photoelectric Effect, Motivation, Operations on Complex Numbers, Polar Coordinates and Complex Phases, Complex Vector Spaces, Orthonormal Bases, Matrices and the Adjoint, The Outer Product, The Completeness Relation, Representing Vectors in Different Bases, Change of Basis, Multiplication and Inverse of Matrices, Matrices Inside Inner Products, Eigenvalues and Eigenvectors, Hermitian Matrices, Unitary Matrices, Normal Matrices, Representing Matrices in Different Bases, Diagonalizable Matrices, Random Variables and Probability Distributions, Conditional Probability, Expected Values, Standard Deviation, Dimensionless and Dimensionful Constants, Hermitian Operators and Observables, Probability Amplitudes, Superposition, Summary For Discrete Systems, The Pauli Matrices, Qubits, The Meaning of Superposition, The Tensor Product, Vectors and Matrices in the Composite Hilbert Space, Quantum Entanglement, The Bell States, Entanglement Does Not Transmit Information, The Uncertainty Principle, Simultaneous Diagonalization, Unitary Transformations and Evolution, Quantum Logic Gates, Applications of the Measurement Axiom, Quantum Teleportation, Exponentials and Logarithms, Matrix and Operator Exponentials, Hamiltonians and Energy, A Quick Review of Classical Hamiltonian Mechanics, Canonical Quantization, The Classical Harmonic Oscillator, Quantizing the Harmonic Oscillator, The Energy Eigenstates of the Harmonic Oscillator, The Position Operator, Wavefunctions in the Position Basis, The Momentum Operator, Quantum Interference, Separation of Variables.
Author(s): Barak Shoshany, Department of Physics, University of Toronto
165Pages
The contents of this pdf note include:Quantum light and the two level system, decaying two level system, Cavity quantum electrodynamics, Fundamentals of laser theory , Cooling of atoms, Cavity optomechanics, Cooling of trapped ions, Collective effects : super/subradiance, Interaction of light with molecules.
Author(s): Claudiu Genes
91Pages
This note covers the following topics: Classical Physics, Waves, Probability Density, The Ultraviolet Catastrophe, Bragg X-ray Diffraction, Wave-Particle Duality, Particles and Fields, Heisenberg’s Uncertainty Principle, Wavefunctions - Schrodinger’s Equation, Quantum Tunnelling, Quantum States and Superposition, Two State Systems, Wavefunction Collapse, Interpretations of Quantum Physics, Probabilistic Determinism.
Author(s): Douglas Ross FRS
97Pages
Quantum physics is a catch-all term for the ideas, devices and technologies made possible by the development of quantum mechanics in the early part of the 20th century. This note concentrates on the ideas behind quantum mechanics itself, but the broader field of quantum physics encompasses everything from the science of electronic devices and lasers to the philosophical mysteries of quantum measurement theory.
Author(s): Matthew Foulkes
104Pages
This note covers the following topics: Time-Independent Non-degenerate Perturbation Theory, Dealing with Degeneracy, Degeneracy, Symmetry and Conservation Laws, Time--dependence, Two state systems, Hydrogen ion and Covalent Bonding, The Variational Principle, Indistinguishable Particles and Exchange, Self-consistent field theory, Fundamentals of Quantum Scattering Theory, Scattering in three dimensions, Quantum Scattering Theory, Partial Waves.
Author(s): Prof. Graeme Ackland
NAPages
An important aspect of the design of this note is to maintain a concise basic treatment of the physics, with derivations and examples available behind hyperlinks. Topics covered includes: The Problems with Classical Physics, Diffraction, Wave Packet, Operators, The Schrodinger Equation, Eigenfunctions, Eigenvalues and Vector Spaces, 3D Problems Separable in Cartesian Coordinates, Hydrogen, 3D Symmetric HO in Spherical Coordinates, Electrons in an Electromagnetic Field, Time Independent Perturbation Theory, Fine Structure in Hydrogen, Atomic Physics, Scattering, Classical Scalar Fields, Quantum Theory of Radiation, Dirac Equation.
Author(s): James G. Branson
548Pages
This note covers the following topics: The Early History of Quantum Mechanics, The Wave Function, The Two Slit Experiment, Wave Mechanics, Particle Spin and the Stern-Gerlach Experiment, Probability Amplitudes, Vector Spaces in Quantum Mechanics, General Mathematical Description of a Quantum System, State Spaces of Infinite Dimension, Operations on States, Matrix Representations of State Vectors and Operators, Probability, Expectation Value and Uncertainty, Time Evolution in Quantum Mechanics.
Author(s): J D Cresser
238Pages
This book is written for anybody who is curious about nature and motion. It covers the following topics: Minimum action: quantum theory for poets, Light: the strange consequences of the quantum of action, Motion of matter: beyond classical physics, The quantum description of matter and its motion, Permutation of particles, Rotations and statistics: visualising spin, Superpositions and probabilities, quantum theory without ideology, Colours and other interactions between light and matter and Quantum physics in a nutshell.
Author(s): Christoph Schiller
270Pages
