The physics of quantum mechanics / James Binney, Rudolf Peierls Centre for Theoretical Physics and Merton College, University of Oxford, David Skinner, Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Cover; Contents; Preface; 1 Introduction; 1.1 Origins; 1.2 Measurements; 1.2.1 Measurement involves disturbance; Heisenberg microscope; 1.2.2 Ideal measurements; 1.2.3 Summary; 1.3 Probability amplitudes; 1.3.1 Two-slit interference; 1.4 Quantum states; 1.4.1 Observables; Complete sets of amplitudes; 1.4.2 Vector spaces and their duals; 1.4.3 The energy representation; 1.4.4 Polarisation of photons; 1.5 Summary; Problems; 2 Operators, measurement and time evolution; 2.1 Operators; Functions of operators; Commutators; 2.2 Evolution in time; 2.2.1 Evolution of expectation values
2.3 The position representation2.3.1 Hamiltonian of a particle; 2.3.2 Wavefunction for well-defined momentum; The uncertainty principle; 2.3.3 Dynamics of a free particle; 2.3.4 Back to two-slit interference; 2.3.5 Generalisation to three dimensions; Probability current; The virial theorem; 2.4 Summary; Problems; 3 Oscillators; 3.1Stationary states of a harmonic oscillator; 3.2 Dynamics of oscillators; 3.2.1 Anharmonic oscillators; Problems; 4 Transformations and observables; 4.1 Transforming kets; 4.1.1 Translating kets; 4.1.2 Continuous transformations and generators
4.1.3 The rotation operator4.1.4 Discrete transformations; The parity operator; Mirror operators; 4.2 Transformations of operators; The parity operator; Mirror operators; 4.3 Symmetries and conservation laws; 4.4The Heisenberg picture; 4.5 What is the essence of quantum mechanics?; Problems; 5 Motion in step potentials; 5.1 Square potential well; 5.1.1 Limiting cases; Infinitely deep well; Infinitely narrow well; 5.2 A pair of square wells; 5.2.1 Ammonia; The ammonia maser; 5.3 Scattering of free particles; The scattering cross-section; 5.3.1 Tunnelling through a potential barrier
5.3.2 Scattering by a classically allowed region5.3.3 Resonant scattering; The Breit-Wigner cross-section; 5.4 How applicable are our results?; 5.5 Summary; Problems; 6 Composite systems; 6.1 Composite systems; 6.1.1 Collapse of the wavefunction; 6.1.2 Operators for composite systems; 6.1.3 Development of entanglement; 6.1.4 Einstein-Podolski-Rosen experiment; Bell's inequality; 6.2 Quantum computing; 6.3 The density operator; 6.3.1 Reduced density operators; 6.3.2 Shannon entropy; 6.4 Thermodynamics; 6.5 Measurement; Problems; 7Angular momentum; 7.1 Eigenvalues of Jz and J2
7.1.1 Rotation spectra of diatomic molecules7.2 Spin and orbital angular momentum; 7.2.1 Orbital angular momentum; L as the generator of circular translations; Spectra of L2 and Lz; 7.2.2 Spin angular momentum; 7.3 Physics of spin; 7.3.1 Spin-half matrices; 7.3.2 Spin-one matrices; 7.3.3 The Stern-Gerlach experiment; Stern-Gerlach experiment with spin-one atoms; 7.3.4 Precession in a magnetic field; 7.3.5 The classical limit; 7.4 Orbital angular-momentum eigenfunctions; 7.4.1 Orbital angular momentum and parity; 7.4.2 Orbital angular momentum and kinetic energy; 7.4.3 Legendre polynomials
Summary
The Physics of Quantum Mechanics aims to give students a good understanding of how quantum mechanics describes the material world. It shows that the theory follows naturally from the use of probability amplitudes to derive probabilities. It stresses that stationary states are unphysical mathematical abstractions that enable us to solve the theory's governing equation, the time-dependent Schroedinger equation. Every opportunity is taken to illustrate the emergence of the familiarclassical, dynamical world through the quantum interference of stationary states. The text stresses the continuity be
