# Introduction to Quantum Mechanics

Phys 451 — Fall 2015 |

Department of Physics & Astronomy |

Instructor | Dr. Kevin Beach |

Office: | 206 Lewis Hall |

Email: | kbeach@olemiss.edu |

Website: | https://www.phy.olemiss.edu/~kbeach |

More details provided in the syllabus.

# Assignments

- due Tuesday, September 15
- due Thursday, October 1
- due Thursday, November 12
- due Thursday, December 3

# Final Exam

Posted below are the second test and final exam from 2014, with partial solutions. The form of our final (on Thursday, December 10 at 8:00) will be similar.

# Lectures

- Review of the syllabus; differences between classical and quantum mechanics in the Lagrangian and Hamiltonian schemes; features of QM that break our classical intuition; probability; averages and variances; probability amplitude; constructive and destructive interference; Dirac notation; quantum states as elements of a linear vector space—see Griffiths 1.1–1.4; Fitzpatrick 2.1–2.5
- orthonormality and completeness of states; time evolution of quantum states; operator formalism; expectation values and matrix elements; position representation and momentum representations as Fourier transform pairs; wave function of a freely propagating particle; current operator and continuity equation for the local probability density—see Griffiths 1.5–1.6, 2.4; Fitzpatrick 3.1–3.16
- Probabilty current arising from a spatially varying phase angle; time evolution of expectation values; commutator relations; stationary states; eigenfunctions and eigenvalues; inner products and the expansion postulate—see Griffiths 2.1,3.1–3.7; Fitzpatrick 4.1–4.12
- Expansion in a complete basis of energy eigenstates; closure relation; normalization; expectation value of energy; measurement postulate; infinite square well; continuity and smoothness of the wave function; reflection symmetry and the parity of the wave function—see Griffiths 2.2; Fitzpatrick 5.1–5.2
- Finite square well; applying matching conditions for a piecewise-defined wave function; particle in a double well; two-level systems—see Griffiths 2.5–2.6; Fitzpatrick 5.7
- Image potential near a metallic surface; exponential envelope in the asymptotic limit; power series solutions; barrier tunnelling problems; transmission and reflection coefficients—see Fitzpatrick 7.1–7.3, 5.8, 9.4, 5.3
- Transfer Matrix approach to barrier tunnelling; mulitple barrier tunnelling events; scanning tunnelling microscopy