**Course title**: **Quantum Mechanics for Engineers** (EE 521)

** **

*“Think quantum”*

**Instructor**

M. P. Anantram (Anant)

anant@uw.edu

Phone: 206-221-5162

**Description**

The focus of this course is to introduce students to quantum mechanics using 1D, 2D and 3D nanomaterials. The students will develop a working knowledge of quantization in quantum dots/wells/wires, band structure, density of states and Fermi’s golden rule (optical absorption, electron- impurity/phonon scattering). Applications will focus on nanodevices and nanomaterials.

**Topics **

1) Schrodinger’s eqn

- Definition
- Interpretation
- Continuity equation for probability density
- Continuity of wave function and its first derivative
- Expectation value
- Uncertainty principle

2) Closed and Open systems (examples of importance to nano devices and materials)

- Particle in a box
- Single Barrier Tunneling (discussion in context of transistors)
- Double Barriers (resonant tunneling diodes)
- Separation of variables
- Nanowire
- Quantum Well
- Quantum Dot
- Coupled quantum wells
- Hydrogen Atom
- Kronig-Penney model
- Time evolution of wave packets

3) Crystalline solid

- Unit cell and Basis vectors
- Real space and Reciprocal space
- Examples: Nanowire, Graphene (2D), 3D solid

4) Energy levels and wave function in a crystalline solid

- Bloch’s theorem
- Basic bandstructure calculation
- Examples of relevance to devices: Carbon nanotube / Silicon nanowire, Graphene, Diamond / Silicon

5) Density of states of open and closed systems

- Atoms, particle in a box, quantum dot
- Free particles in 1D, 2D and 3D
- Nanowire and quantum wells within an effective mass framework
- Graphene in a tight binding framework
- Nanotubes in a tight binding framework

6) Spins

- Stern-Gerlach experiment
- Hamiltonian of a nanostructure in a magnetic field
- Example of spintronic device

7) Perturbation theory

- First order and second order perturbation theory
- Fermi’s Golden rule and applications of relevance to devices: Electron-impurity interaction, Electron-phonon interaction, Relationship to mobility, Optical absorption / dipole matrix elements

**Books**

- Detailed Course slides
- The following books will be useful:
- Quantum Mechanics for Engineering: Materials Science and Applied Physics, Herbert Kroemer, Prentice Hall
- Quantum Transport: Atom to Transistor, Supriyo Datta, Cambridge University Press

**Learning Objectives**

- Learning to
*think quantum*so as to aid reading literature involving nanotechnology - Developing the ability to perform simple quantum calculations that are important to both experimentalists and theorists
- Meaning and solutions of Schrodinger’s wave equation

- Calculate basic expressions for tunneling through barriers and resonant tunneling phenomena
- Numerical solution of Schrodinger’s equation as relevant to experimental students
- Learning to calculate the role of quantization in technological relevant examples: quantum dots, nanowires, quantum wells
- De Broglie’s Uncertainity Principle and Energy-Time Uncertainity Principle
- Method of separation of variables
- Basics of the tight binding method
- Learning to apply Bloch’s theorem in bulk and nanomaterials to calculate the bandstructure
- Density of states
- Basics of spins and representation of logic states using spins
- Derivation and application of Fermi’s golden rule for transition rates. Examples will include electron-photon interaction / optical absorption and electron-impurity/phonon scattering