The Physics of Quantum Mechanics, Binney and Skinner - The Physics of Quantum Mechanics James Binney and David Skinner iv Copyright c 2008 James Binney

The Physics of Quantum Mechanics, Binney and Skinner - The...

  • Test Prep
  • migabrael2
  • 277
  • 0% (2) 0 out of 2 people found this document helpful

This preview shows page 1 - 5 out of 277 pages.

The Physics of Quantum Mechanics James Binney and David Skinner
Image of page 1
iv Copyright c circlecopyrt 2008 James Binney and David Skinner Published by Capella Archive 2008
Image of page 2
Contents Preface ix 1 Probability and probability amplitudes 1 1.1 The laws of probability 4 Expectation values 5 1.2 Probability amplitudes 6 Two-slit interference 8 Matter waves? 9 1.3 Quantum states 10 Quantum amplitudes and measurements 10 Complete sets of amplitudes 11 Dirac notation 12 Vector spaces and their adjoints 13 The energy rep- resentation 16 Orientation of a spin-half particle 17 Polarisation of photons 18 1.4 Measurement 20 Problems 21 2 Operators, measurement and time evolution 23 2.1 Operators 24 Functions of operators 27 Commutators 28 2.2 Evolution in time 29 Evolution of expectation values 31 2.3 The position representation 32 Hamiltonian of a particle 35 Wavefunction for well defined momentum 37 The uncertainty principle 38 Dynamics of a free particle 39 Back to two-slit in- terference 41 Generalisation to three dimensions 43 The virial theorem 43 Problems 45 3 Harmonic oscillators and magnetic fields 49 3.1 Stationary states of a harmonic oscillator 50 3.2 Dynamics of oscillators 54 Anharmonic oscillators 55 3.3 Motion in a magnetic field 59 Gauge transformations 61 Landau Levels 63 Displacement of the gyrocentre 65 Aharonov-Bohm ef- fect 67 Problems 70 4 Transformations & Observables 76 4.1 Transforming kets 77 Translating kets 77 Continuous transformations and generators 80 The rotation operator 82 Discrete transformations 82
Image of page 3
vi Contents 4.2 Transformations of operators 84 4.3 Symmetries and conservation laws 89 4.4 The Heisenberg picture 91 4.5 What is the essence of quantum mechanics? 92 Problems 95 5 Motion in step potentials 97 5.1 Square potential well 97 Limiting cases 101 (a) Infinitely deep well 101 (b) Infinitely narrow well 102 5.2 A pair of square wells 103 Ammonia 106 The ammonia maser 107 5.3 Scattering of free particles 110 Reflection off a potential well 110 Tunnelling through a potential barrier 113 5.4 What we have learnt 115 Problems 117 6 Composite systems 122 6.1 Composite systems 123 Collapse of the wavefunction 128 Operators for com- posite systems 129 Development of entanglement 131 Einstein–Podolski–Rosen experiment 132 Bell’s inequality 134 6.2 Quantum computing 138 6.3 The density operator 145 Reduced density operators 150 Shannon entropy 153 Thermodynamics 156 6.4 Measurement 159 Problems 161 7 Angular Momentum 166 7.1 Eigenvalues of J z and J 2 167 Rotation spectra of diatomic molecules 170 7.2 Orbital angular momentum 174 L as the generator of circular translations 175 Spectra of L 2 and L z 177 Orbital angular momentum eigenfunc- tions 177 Orbital angular momentum and parity 182 Orbital angular momentum and kinetic energy 183 Legendre polynomials 185 7.3 Three-dimensional harmonic oscillator 186 7.4 Spin angular momentum 192 Spin and orientation 193 Spin-half systems 195 The
Image of page 4
Image of page 5

You've reached the end of your free preview.

Want to read all 277 pages?

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes