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