The aim of this course is to present the elements of quantum mechanics that are essential for understanding many areas in modern optics and photonics. This course will be useful background for pursuing more advanced courses in optoelectronics, solid state physics, semiconductor optics, and nonlinear optics, and essential background for studying quantum optics. Prerequisites for the class are linear algebra, advanced calculus and partial differential equations, and general physics.

**Pre-requisites: **Graduate Standing or Consent of Instructor

**Suggested textbooks**

- D. A. B. Miller, “Quantum Mechanics for Scientists and Engineers,” (Cambridge University Press, 2008)”
- H. Kroemer, “Applied Quantum Mechanics for Engineering, Materials Science, and Applied Physics” (Prentice Hall, New Jersey, 1994).
- R. Gilmore, “Quantum Mechanics in One Dimension” (The Johns Hopkins University Press, 2004).

**Outcomes**

Upon completion of the course, students will be able to analyze optical processes and optoelectronic devices in a quantum mechanical framework. The students will be familiar with the main quantum mechanical concepts that will allow them to pursue more advanced courses in quantum optics, semiconductor and solid-state physics, and modern optoelectronic and nanophotonic devices.

**Grading**

- 40% homework
- 30% midterm
- 30% final

**Course Syllabus**:

- Historical development of quantum mechanics in the context of optics
- What is a photon?
- The photo-electric effect
- Atomic spectra
- The Frank-Hertz experimentv
- The Compton effect
- Wave-particle duality
- The emergence of quantum mechanics

- Introduction to quantum mechanics
- Mathematical background
- Linear vector spaces
- Hermitian operators
- Unitary transformations
- Eigenvalue problems

- Axioms of quantum mechanics
- Examples of dynamical variables
- Schrodingerâ€™s equation

- Schrodingerâ€™s equation in one dimension
- Translational motion
- The harmonic oscillator
- Transfer matrix analysis: potential barriers and tunneling
- Quantum wells, quantum wires
- Boundary conditions for scattering, bound, and periodic states
- Degenerate states, impurity states, density of states
- Energy band gaps in periodic multilayer systems

- Schrodingerâ€™s equation in two and three dimensions
- Particle on a ring
- Hydrogen atom
- Angular momentum
- Electron spin

- Approximation methods
- Time-independent perturbation theory
- Variational theory
- Time-dependent perturbation theory
- Helium atom
- Hydrogen molecule
- Molecular orbitals (LUMO and HOMO)
- Transition rates and the Einstein coefficients

- Relaxation and dissipation in quantum mechanics
- Density matrix formalism
- Lifetime and decoherence
- Fluoresence and luminescence
- Raman scattering
- Nonlinear optics

- Examples of how quantum mechanics enters into device design
- Modern research on the foundations of quantum mechanics
- The EPR paradox
- Bellâ€™s inequality
- Quantum cryptography and communications
- Quantum computing

- So, what IS a photon?