Quantum Mechanics for Nuclear Structure, Volume 1: A Primer

Description

This book offers a detailed introduction into the field of quantum mechanics applied to nuclear structure, and is intended for as a primer for nuclear physics graduate students and postgraduate students seeking a solid foundation in the subject. PRELIMS.pdf Preface Author biographies Kris Heyde John L Wood CH001.pdf Chapter 1 A theory of polarized photons 1.1 Polarized lightwaves 1.2 Polarized photons 1.3 Uncertainty in experiments 1.4 Dirac bracket notation 1.5 Transformation properties of polarizing filter measurements 1.6 Multiples of kets 1.7 Exercises Reference CH002.pdf Chapter 2 A theory of the Stern–Gerlach experiment for spin-12 particles 2.1 The Stern–Gerlach experiment 2.2 Sequences of Stern–Gerlach measurements 2.3 State representation for spin-12 particles 2.3.1 Representation with respect to mutually orthogonal axes Example 2.1 Example 2.2 Example 2.3 2.3.2 Representation with respect to arbitrary axes 2.4 The choice of basis kets 2.5 Exercises 2.6 An introduction to operators for spin-12 particles 2.6.1 Outer products of kets and bras as operators 2.6.2 Column vectors, row vectors, and matrices 2.6.3 Non-commutation of operators 2.6.4 The cone of uncertainty for quantum spin-12 particles 2.7 Exercises Reference CH003.pdf Chapter 3 The axioms of quantum mechanics 3.1 Global axioms of observation 3.2 Axioms for quantum mechanical observations 3.3 Axioms for the mathematical structure of quantum mechanics 3.4 Axioms for the incorporation of ℏ in quantum mechanics 3.5 Exercise CH004.pdf Chapter 4 Linear spaces and linear operators 4.1 Definitions and theorems for linear spaces and linear operators 4.2 Linear spaces, Dirac bras and kets, and operators 4.3 Outer products of Dirac bras and kets 4.4 Exercises CH005.pdf Chapter 5 The harmonic oscillator 5.1 The quantum mechanical one-dimensional harmonic oscillator 5.2 The quantum mechanical two-dimensional harmonic oscillator 5.3 Time dependence of the one-dimensional quantum harmonic oscillator 5.4 Exercises 5.5 Coherent states and the one-dimensional harmonic oscillator CH006.pdf Chapter 6 Representations: matrices 6.1 Basics of matrix manipulation 6.2 Exercises 6.3 The two-level mixing problem 6.4 Exercises 6.5 Unitary transformations and matrix diagonalization 6.6 Exercises 6.7 Matrix diagonalization: the Jacobi method 6.7.1 Example 6.8 Exercise References CH007.pdf Chapter 7 Observables and measurements 7.1 Basic concepts 7.2 The uncertainty relation 7.3 Exercises 7.4 Mixtures and the density matrix CH008.pdf Chapter 8 Representations: position, momentum, wave functions, and function spaces 8.1 The concept of a wave function 8.2 The quantum mechanical structure of position and momentum 8.3 The wave-like properties of matter 8.4 Exercises References CH009.pdf Chapter 9 Quantum dynamics: time evolution and the Schrödinger and Heisenberg pictures 9.1 Basic relations 9.2 Spin precession 9.3 Exercises 9.4 Correlation amplitude and the energy–time uncertainty relation 9.5 The Schrödinger and Heisenberg pictures 9.6 The free particle in the Heisenberg picture 9.7 Schrödinger’s wave equation 9.8 Exercises 9.9 Alternative derivation of the energy–time uncertainty relation 9.10 Time-dependent phenomena 9.11 Time-dependent two-state problems 9.12 Exercise Reference CH010.pdf Chapter 10 Rotations and continuous transformation groups 10.1 Elements of group theory 10.2 Matrix groups 10.3 Exercises 10.4 Rotations in physical space 10.5 Exercise 10.6 Rotations of quantum mechanical states 10.7 Exercise CH011.pdf Chapter 11 Angular momentum and spin in quantum mechanics 11.1 The algebra of angular momentum in quantum mechanics 11.2 Algebraic solution of the quantum mechanical angular momentum problem 11.3 Exercises CH012.pdf Chapter 12 Central force problems 12.1 General features of central force problems 12.2 Central force problems, factorization algebra and isospectral Hamiltonians 12.3 The hydrogen atom central force problem 12.4 The three-dimensional isotropic harmonic oscillator central force problem 12.5 The three-dimensional isotropic infinite square well central force problem 12.6 Exercises 12.7 Central force problems and so(2, 1) or su(1, 1) algebra 12.8 so(2, 1) solution for the hydrogen atom Comments 12.9 so(2, 1) solution for the three-dimensional isotropic harmonic oscillator References CH013.pdf Chapter 13 Motion of an electron in a uniform magnetic field 13.1 Maxwell’s equations 13.2 The Landau level problem 13.3 Time dependence of the Landau problem 13.4 Exercises Reference APP1.pdf Chapter A.1 Basic definitions A.2 Secondary relations APP2.pdf Chapter B.1 Hydrogen atom B.2 Three-dimensional isotropic harmonic oscillator