The Physics of Quantum Mechanics 1st edition by James Binney, David Skinner – Ebook PDF Instant Download/Delivery: 0191002274 , 9780191002274
Full download The Physics of Quantum Mechanics 1st edition after payment
Product details:
ISBN 10: 0191002274
ISBN 13: 9780191002274
Author: James Binney, David Skinner
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 familiar classical, dynamical world through the quantum interference of stationary states. The text stresses the continuity between the quantum world and the classical world, which is merely an approximation to the quantum world. The connections between observables, operators and transformations are clearly explained and the standard commutation rules derived from the properties of spacetime. A chapter is devoted to entanglement, quantum computation, density operators and their role in thermodynamics, and the measurement problem. Scattering phenomena, including the origin of radioactivity, are handled early on in the accessible context of one dimension, and at the end of the book with some rigour in three dimensions. Hydrogen and helium are discussed in some detail and it is shown that quantum mechanics enables us to understand the structure of the periodic table without engaging with the complexities of many-electron atoms. Dirac notation is used from the outset and students are trained to move easily from one representation to another, choosing whichever representation is best suited to a particular problem. The mathematical prerequisites are no more than simple vector algebra, Taylor series expansion and the use of integrating factors to solve linear first order differential equations. Rigorous algebraic methods are preferred to the solution of partial differential equations.
The Physics of Quantum Mechanics 1st Table of contents:
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 representation
2.3.1 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
3.1 Stationary 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 operator
4.1.4 Discrete transformations
The parity operator
Mirror operators
4.2 Transformations of operators
The parity operator
Mirror operators
4.3 Symmetries and conservation laws
4.4 The 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 region
5.3.3 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
7 Angular momentum
7.1 Eigenvalues of Jz and J2
7.1.1 Rotation spectra of diatomic molecules
7.2 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
7.5 Three-dimensional harmonic oscillator
7.6 Addition of angular momenta
7.6.1 Case of two spin-half systems
7.6.2 Case of spin-one and spin-half
7.6.3 The classical limit
Problems
8 Hydrogen
8.1 Gross structure of hydrogen
8.1.1 Emission-line spectra
8.1.2 Radial eigenfunctions
8.1.3 Shielding
8.1.4 Expectation values for r−k
8.2 Fine structure and beyond
8.2.1 Spin–orbit coupling
8.2.2 Hyperfine structure
Problems
9 Motion in a magnetic field
9.1 Hamiltonian for motion in a magnetic field
9.1.1 Classical equations of motion
9.2 Gauge transformations
9.2.1 Probability current
9.3 Landau levels
9.3.1 Displacement of the gyrocentre
9.4 Aharonov–Bohm effect
Problems
10 Perturbation theory
10.1 Time-independent perturbations
10.1.1 Quadratic Stark effect
10.1.2 Linear Stark effect and degenerate perturbation theory
10.1.3 Effect of an external magnetic field
Paschen–Back effect
Zeeman effect
10.2 Variational principle
10.3 Time-dependent perturbation theory
10.3.1 Fermi golden rule
10.3.2 Radiative transition rates
10.3.3 Selection rules
Problems
11 Helium and the periodic table
11.1 Identical particles
Generalisation to the case of N identical particles
11.1.1 Pauli exclusion principle
11.1.2 Electron pairs
11.2 Gross structure of helium
11.2.1 Gross structure from perturbation theory
11.2.2 Application of the variational principle to helium
11.2.3 Excited states of helium
11.2.4 Electronic configurations and spectroscopic terms
Spectrum of helium
11.3 The periodic table
11.3.1 From lithium to argon
11.3.2 The fourth and fifth periods
Problems
12 Adiabatic principle
12.1 Derivation of the adiabatic principle
12.2 Application to kinetic theory
12.3 Application to thermodynamics
12.4 The compressibility of condensed matter
12.5 Covalent bonding
12.5.1 A model of a covalent bond
12.5.2 Molecular dynamics
12.5.3 Dissociation of molecules
12.6 The WKBJ approximation
Problems
13 Scattering theory
13.1 The scattering operator
13.1.1 Perturbative treatment of the scattering operator
13.2 The S-matrix
13.2.1 The iϵ prescription
13.2.2 Expanding the S-matrix
13.2.3 The scattering amplitude
13.3 Cross-sections and scattering experiments
13.3.1 The optical theorem
13.4 Scattering electrons off hydrogen
13.5 Partial wave expansions
13.5.1 Scattering at low energy
13.6 Resonant scattering
13.6.1 Breit–Wigner resonances
13.6.2 Radioactive decay
Problems
Appendices
A The laws of probability
B Cartesian tensors
C Fourier series and transforms
D Operators in classical statistical mechanics
E Lie groups and Lie algebras
F The hidden symmetry of hydrogen
G Lorentz covariant equations
H Thomas precession
I Matrix elements for a dipole–dipole interaction
J Selection rule for j
K Direct and exchange integrals for helium
L Restrictions on scattering potentials
Index
People also search for The Physics of Quantum Mechanics 1st :
the physics of quantum mechanics pdf
the physics of quantum mechanics binney solutions
introduction to the maths and physics of quantum mechanics
quantum mechanics the physics of the microscopic world
bohmian mechanics the physics and mathematics of quantum theory
Tags: James Binney, David Skinner, The Physics, Quantum Mechanics