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Quantum Mechanics for Scientists and Engineers

Introduction:Quantum mechanics and real life, Quantum mechanics as an intellectual achievement
Waves and quantum mechanics – Schrödinger’s equation:Diffraction by two slits
The time-dependent Schrödinger equation:Quantum mechanical measurement and expectation values
Functions and operators:Bilinear expansion of linear operators, Hermitian operators
Operators and quantum mechanics:Commutation of operators, General form of the uncertainty principle
Approximation methods in quantum mechanics:Degenerate perturbation theory, Variational method
Time-dependent perturbation theory:Simple oscillating perturbations, Refractive index
Quantum mechanics in crystalline materials:One electron approximation, Band structure
Angular momentum:L squared operator, Visualization of angular momentum
The hydrogen atom:Multiple particle wavefunctions, Coordinates for the hydrogen atom problem
Methods for one-dimensional problems:Transfer matrix, Electron emission with a potential barrier
Spin:Angular momentum and magnetic moments, Direct product spaces and wavefunctions with spin
Identical particles:Pauli exclusion principle, Extension to more than two identical particles
The density matrix:Pure and mixed states, Time-evolution of the density matrix
Harmonic oscillators and photons:Quantization of electromagnetic fields, Field operators
Fermion operators:Postulation of fermion annihilation and creation operators, Wavefunction operator
Interaction of different kinds of particles:Operators for systems with different kinds of particles
Quantum information:Quantum mechanical measurements and wavefunction collapse, Quantum computing
Interpretation of quantum mechanics:Hidden variables and Bell’s inequalities, Epilogue
Appendix A Background mathematics:Exponential and logarithm notation
Appendix B Background physics:Elementary classical mechanics, Waves and diffraction
Appendix C Vector calculus:Spherical polar coordinates, Cylindrical coordinates
Appendix D Maxwell’s equations and electromagnetism:Maxwell’s equations in free space
Appendix E Perturbing Hamiltonian for optical absorption:Quantum mechanical Hamiltonian
Appendix F Early history of quantum mechanics
Appendix G Some useful mathematical formulae:Formulae for sines, cosines, and exponentials
Appendix H Greek alphabet
Appendix I Fundamental constants
Memorization list

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