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## Quantum Mechanics: A Paradigms Approach

We have written a Quantum Mechanics textbook that reflects the way we teach the subject in our junior-year Paradigms courses and our senior-year Capstone course. The text is published by Addison-Wesley and is supported by our extensive student engagement activities. If you have any questions about material on this page or see any errors, please contact me via email . This material is based upon work supported by the National Science Foundation under Grant No. 0618877. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Quantum Mechanics: A Paradigms Approach David H. McIntyre Pearson Addison-Wesley © 2012 ISBN-10: 0-321-76579-6 ISBN-13: 978-0-321-76579-6 |

### Instructor Resources

- Activities
- All QM activities organized by textbook chapters or by concepts
- SPINS software
- SPINS activities

- OSU Paradigms courses
- Instructor's Guide for Spin and Quantum Measurement course (PH 425) (1st 3 chapters of book)

- Animations of figures in the text
- Solutions Manual: Available to instructors at Pearson web site under resources tab. (Please contact me via email if you find any errors.)
- Reviews of the book
- Times Higher Education 24 May 2012
- American Journal of Physics Vol. 80, pp. 650-651, July 2012

- Errata as of 5 January 2017

### Table of Contents

- Stern-Gerlach Experiments
- Operators and Measurement
- Schrödinger Time Evolution
- Quantum Spookiness
- Quantized Energies:Particle in a Box
- Unbound States
- Angular Momentum
- Hydrogen Atom
- One-dimensional Harmonic Oscillator
- Time-Independent Perturbation Theory
- Hyperfine Structure and the Addition of Angular Momentum
- Perturbation of Hydrogen
- Identical Particles
- Time-Dependent Perturbation Theory
- Periodic Potentials
- Modern Applications of Quantum Mechanics

- Appendices
- A. Probability
- B. Complex Numbers
- C. Linear Algebra and Matrices
- D. Waves and Fourier Analysis
- E. Separation of Variables
- F. Integrals
- G. Physical Constants

### OSU course structure

At Oregon State University, the content of this quantum text is taught in five courses as shown below. Some courses include non quantum material (shown in *italics*).

Junior-Year Paradigms Courses | |||
---|---|---|---|

Spin and Quantum Measurement PH 425 | Waves PH 424 | Central Forces PH 426 | Period Systems PH 427 |

1. Stern-Gerlach Experiments | Mechanical waves and EM waves | Planetary orbits | Coupled Oscillations |

2. Operators and Measurement | 5. Quantized Energies: Particle in a Box | 7. Angular Momentum | 15. Periodic Systems |

3. Schrödinger Time Evolution | 6. Unbound States | 8. Hydrogen Atom | |

4. Quantum Spookiness | |||

Senior-Year Quantum Mechanics Capstone Course PH 451 | |||

9. Harmonic Oscillator | 11. Hyperfine Structure and the Addition of Angular Momentum | 13. Identical Particles | 16. Modern Applications |

10. Perturbation Theory | 12. Perturbation of Hydrogen | 14. Time-Dependent Perturbation Theory |

### Weekly Curriculum for Semesters or Quarters

For a traditional curriculum, the content of this text would cover a full-year course, either two semesters or three quarters. A proposed weekly outline for two 15-week semesters or three 10-week quarters is shown below.

Week | Chapter | Topics |
---|---|---|

1 | 1 | Stern-Gerlach experiment, Quantum State Vectors, Bra-ket notation |

2 | 1 | Matrix notation, General Quantum Systems |

3 | 2 | Operators, Measurement, Commuting Observables |

4 | 2 | Uncertainty Principle, S^{2} Operator, Spin-1 System |

5 | 3 | Schrödinger Equation, Time Evolution |

6 | 3 | Spin Precession, Neutrino Oscillations, Magnetic Resonance |

7 | 4 | EPR Paradox, Bell's Inequalities, Schrödinger's Cat |

8 | 5 | Energy Eigenvalue Equation, Wave Function |

9 | 5 | One-Dimensional Potentials, Finite Well, Infinite Well |

10 | 6 | Free Particle, Wave Packets, Momentum Space |

11 | 6 | Uncertainty Principle, Barriers |

12 | 7 | Three-Dimensional Energy Eigenvalue Equation, Separation of Variables |

13 | 7 | Angular Momentum, Motion on a Ring and Sphere, Spherical Harmonics |

14 | 8 | Hydrogen Atom, Radial Equation, Energy Eigenvalues |

15 | 8 | Hydrogen Wave Functions, Spectroscopy |

16 | 9 | 1-D Harmonic Oscillator, Operator Approach, Energy Spectrum |

17 | 9 | Harmonic Oscillator Wave Functions, Matrix Representation |

18 | 9 | Momentum Space Wave Functions, Time Dependence, Molecular Vibrations |

19 | 10 | Time-Independent Perturbation Theory: Nondegenerate, Degenerate |

20 | 10 | Perturbation Examples: Harmonic Oscillator, Stark Effect in Hydrogen |

21 | 11 | Hyperfine Structure, Coupled Basis |

22 | 11 | Addition of Angular Momentum, Clebsch-Gordan Coefficients |

23 | 12 | Hydrogen Atom: Fine Structure, Spin-Orbit, Zeeman Effect |

24 | 13 | Identical Particles, Symmetrization, Helium Atom |

25 | 14 | Time-Dependent Perturbation Theory, Harmonic Perturbation |

26 | 14 | Radiation, Selection Rules |

27 | 15 | Periodic Potentials, Bloch's Theorem |

28 | 15 | Dispersion Relation, Density of States, Semiconductors |

29 | 16 | Modern Applications of Quantum Mechanics, Laser Cooling and Trapping |

30 | 16 | Quantum Information Processing |