Modern Quantum Physics: A Practical Applications Approach

PRELIMS.pdf
	Preface
	Acknowledgement
	Author biography
		J S Faulkner
CH001.pdf
	Chapter 1 Review of basics
		1.1 About quantum mechanics
		1.2 Hilbert space
		1.3 Elementary quantum mechanics
		1.4 Dirac and von Neumann
		1.5 Rigged Hilbert space
		1.6 Observables and Hermitean operators
		1.7 The uncertainty relation
		1.8 Commuting observables
		1.9 Unitary operators
		1.10 The Gaussian wave packet
		1.11 Two-dimensional Hilbert space
		1.12 Pairs of spins
		1.13 Einstein, Podolsky, and Rosen
		Problems
		References
CH002.pdf
	Chapter 2 Non-relativistic quantum mechanics
		2.1 Heisenberg’s matrix mechanics
		2.2 The one-dimensional harmonic oscillator
		2.3 Schrödinger’s wave mechanics
		2.4 The one-dimensional harmonic oscillator (again)
		2.5 Comparison of Heisenberg and Schrödinger theories
		2.6 Wave mechanics in three dimensions
		2.7 Angular momentum
		2.8 Schrödinger equation for a spherically symmetric potential
		2.9 Schrödinger equation for the hydrogen atom
		2.10 Time-dependent wave equation
		2.11 The time-evolution operator
		2.12 The time dependence of Heisenberg’s operators
		Problems
		References
CH003.pdf
	Chapter 3 Relativistic quantum mechanics
		3.1 The necessity for relativistic quantum mechanics
		3.2 Klein–Gordon equation
		3.3 Problems with the Klein–Gordon equation
		3.4 Dirac theory
		3.5 Proof of the Lorentz covariance of the Dirac equation
		3.6 The fifth gamma matrix
		3.7 Free particle solution of the Dirac equation
		3.8 Angular momentum and spin
		3.9 The magnetic moment of the electron
		3.10 Scalar relativistic approximation
		3.11 The Dirac theory of the hydrogen atom
		3.12 Advantages and disadvantages
		Problems
		References
CH004.pdf
	Chapter 4 Symmetry
		4.1 The importance of symmetry in physics
		4.2 A simple example
		4.3 Theory of finite groups
		4.4 Representations of finite groups
		4.5 Theory of infinite groups and Lie groups
		4.6 Continuous groups in physics
		4.7 Conservation laws from Noether’s theorem
		4.8 Conservation laws from quantum mechanics
		4.9 Continuous group representations
		4.10 Groups of a Hamiltonian
		4.11 Conclusions
		Problems
		References
CH005.pdf
	Chapter 5 Approximate methods
		5.1 Rayleigh–Ritz variational method
		5.2 Time-independent perturbation theory
		5.3 Time-dependent perturbation theory
		5.4 The two-level Hamiltonian
		5.5 Spin magnetic resonance
		5.6 The maser
		5.7 Fermi’s golden rule
		5.8 An atom interacting with a plane electromagnetic wave
		5.9 Approximate methods that use computers
		Problems
		References
CH006.pdf
	Chapter 6 Scattering and Green’s functions
		6.1 Potential scattering
		6.2 Position representation
		6.3 The spherical scatterer
		6.4 The optical theorem
		6.5 The Born approximation
		6.6 Green’s function and its adjoint
		6.7 Green’s function with a scatterer
		6.8 The non-spherical scattering potential with bounded domain
		6.9 Spectral theory from scattering theory
		6.10 Krein’s theorem
		Problems
		References
CH007.pdf
	Chapter 7 A practical tool
		7.1 The exact equations
		7.2 Pauli exclusion principle
		7.3 Atomic structure
		7.4 The hydrogen molecule
		7.5 Covalent bonding
		7.6 Ionic bonding
		7.7 Bonding in metals
		7.8 Conclusions
		Problems
		Reference
CH008.pdf
	Chapter 8 An alternative reality
		8.1 Gazing in wonder
		8.2 The Einstein–Podolsky–Rosen experiment
		8.3 Hidden variables
		8.4 Bell’s inequalities
		8.5 Double slit interference
		8.6 The adiabatic theorem
		8.7 The Bohm–Aharanov phase
		8.8 The Berry phase
		8.9 Quantum erasure
			8.9.1 First experiment
			8.9.2 Quarter-wave plate
			8.9.3 Second experiment
			8.9.4 Third experiment
			8.9.5 Fourth experiment
		8.10 Resume
		Problems
		References
CH009.pdf
	Chapter 9 What does it all mean?
		9.1 What are we to make of quantum experiments?
		9.2 The Orthodox Copenhagen interpretation (Bohr)
		9.3 Bohm’s interpretation
		9.4 The many-worlds interpretation
		9.5 The Ghirardi–Rimini–Weber (GRW) interpretation
		9.6 Consistent (decoherent) histories interpretation
		9.7 Most widely held interpretation
		9.8 Decoherence
		9.9 Density matrices
		9.10 Defining decoherence
		9.11 Simple example of decoherence
		9.12 Back to Schrödinger’s cat
		Problems
		References
CH010.pdf
	Chapter 10 Quantum information
		10.1 Information science
		10.2 Turing machine
		10.3 Bits and bytes and Boolean gates
		10.4 Universality
		10.5 Measuring information
		10.6 Landauer’s theory of the energy required for calculations
		10.7 Reversible computing
		10.8 Universality
		10.9 Zero power computing
		10.10 Computational complexity
		10.11 Quantum devices
		10.12 Quantum bits (qubits)
		10.13 Single qubit gates
		10.14 Random number generator
		10.15 A two qubit gate
		10.16 No cloning theorem
		10.17 Bell or EPR states
		10.18 Entanglement and disentanglement
		10.19 Quantum teleportation
		10.20 Superdense coding
		10.21 Deutsch’s algorithm
		10.22 Deutsch–Jozsa algorithm
		10.23 Four-level Deutsch–Jozsa experiment
		10.24 Discrete Fourier transform
		10.25 The quantum Fourier transform
		Problems
		Reference
CH011.pdf
	Chapter 11 Quantum cryptography
		11.1 The Caesar cipher
		11.2 Symmetric key cryptography
		11.3 Public-key cryptography (asymmetric cryptography)
		11.4 Modular arithmetic
		11.5 RSA public key system. Rivest, Shamir, Adleman
		11.6 Diffie–Hellman key exchange
		11.7 Discrete logarithm problem
		11.8 ElGamal
		11.9 Elliptic curves
		11.10 The Vernam cipher
		11.11 Quantum key distribution
		11.12 Shor factoring algorithm
		Problems
		References
CH012.pdf
	Chapter 12 Many particle systems
		12.1 The Schrödinger equation
		12.2 Hartree theory
		12.3 Hartree–Fock theory
		12.4 Configuration interaction (CI) calculations
		12.5 The electron gas in the Hartree–Fock approximation
		12.6 Critique of the H-F approximation
		12.7 Density matrices
		12.8 Single configuration approximation
		12.9 The Thomas–Fermi and Thomas–Fermi–Dirac theories
		12.10 The density functional theory (DFT)
		12.11 The local density approximation (LDA)
		12.12 Beyond the density functional theory
		12.13 Infinite-order perturbation theory and Feynman diagrams
		12.14 Dielectric function of a degenerate electron gas
		12.15 Progress requires cooperation
		Problems
		References