## Advanced Visual Quantum Mechanics (Google eBook)Advanced Visual Quantum Mechanics is a systematic effort to investigate and to teach quantum mechanics with the aid of computer-generated animations. Although it is self-contained, this book is part of a two-volume set on Visual Quantum Mechanics. The first book appeared in 2000, and earned the European Academic Software Award in 2001 for oustanding innovation in its field. While topics in book one mainly concerned quantum mechanics in one- and two-dimensions, book two sets out to present three-dimensional systems, the hydrogen atom, particles with spin, and relativistic particles. It also contains a basic course on quantum information theory, introducing topics like quantum teleportation, the EPR paradox, and quantum computers. Together the two volumes constitute a complete course in quantum mechanics that places an emphasis on ideas and concepts, with a fair to moderate amount of mathematical rigor. The reader is expected to be familiar with calculus and elementary linear algebra. Any further mathematical concepts will be illustrated in the text. This book has a home page (http://vqm.uni-graz.at) that includes more supplementary material, additional animations and visualizations, Mathematica® notebooks, and further information.' |

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### Contents

Spherical Symmetry | 1 |

Coulomb Problem | 57 |

Particles with Spin | 113 |

Qubits | 157 |

Composite Systems | 211 |

Quantum Information Theory | 271 |

Relativistic Systems in One Dimension | 323 |

The Dirac Equation | 377 |

Appendix B Perturbation of Eigenvalues | 443 |

Analytic Perturbation Theory | 455 |

Variational Method | 461 |

Appendix E Adiabatic and Geometric Phases | 467 |

Appendix F Formal Scattering Theory | 475 |

491 | |

List of Symbols | 505 |

Appendix A Synopsis of Quantum Mechanics | 433 |

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### Common terms and phrases

Alice and Bob angle angular-momentum operators assume belonging Bob’s classical components consider constant corresponding Coulomb problem defined denote density operator described dimensions Dirac equation Dirac operator Dirac spinor eigenfunctions eigenspace eigenstates eigenvalue eigenvector electron ensemble entangled evolution example Exercise expectation value Figure free-particle Dirac Gaussian given Hamiltonian Hence Hilbert space hydrogen atom interferometer Lorentz magnetic field magnetic moment matrix measurement momentum space motion negative energy nonrelativistic nonzero observable obtain orbital angular momentum orthogonal orthonormal basis oscillator parameter Pauli perturbation photons physical plane waves positive energy potential projection operator quantum mechanics quantum number qubit radial relativistic result rotation scalar product Schrödinger equation Section self-adjoint shows solution spherical coordinates spin-up square-integrable standard representation Stern-Gerlach apparatus subspace subsystem superposition symmetry transformation tensor product theorem theory two-particle two-qubit system unitary transformation variables velocity visualizations wave function wave packet