ECE 487 - Introduction to Quantum Electronics

Semesters Offered

Official Description

Application of quantum mechanical concepts to electronics problems; detailed analysis of a calculable two-state laser system; incidental quantum ideas bearing on electronics. Course Information: 3 undergraduate hours. 3 graduate hours. Prerequisite: PHYS 485.

Subject Area

Microelectronics and Photonics

Description

In this course, quantum mechanical concepts are applied to practical problems in physics, electronics, chemistry, and electrical engineering. The goal of this course is to develop the quantum mechanical foundation for modern electronic devices (MEMS, lasers, transistors, LEDs, quantum size effects in FETs, optical communication, etc.).

Goals

Develop a basis for understanding quantum mechanics and its applications in modern electronics and information processing (lasers, field effect transistors, quantum communication, quantum computation, etc.)

Topics

  • time-independent Schrodinger equation
  • quantum mechanical tunneling
  • bound states and scattering
  • transmission electron microscopy
  • the energy spectrum of diatomic and aromatic molecules
  • the band structure of one-dimensional crystalline and disordered solids
  • perturbation theory and field quantization
  • two-state lasers
  • qubits
  • quantum entanglement
  • quantum computation and quantum algorithms

Detailed Description and Outline

Develop a basis for understanding the quantum mechanical aspects of modern electronics (lasers, quantized Hall effect, field effect transistors, optical tweezers, etc.)

Topics:

  • time-independent Schrodinger equation
  • quantum mechanical tunneling
  • bound states and scattering
  • transmission electron microscopy
  • the energy spectrum of diatomic and aromatic molecules
  • the band structure of one-dimensional crystalline and disordered solids
  • perturbation theory and field quantization
  • two-state lasers
  • qubits
  • quantum entanglement
  • quantum computation and quantum algorithms

Texts

Class notes
Recommended: D. Miller, Quantum Mechanics for Scientists and Engineers, Cambridge, 2008.

ABET Category

Engineering Science: 3 credits

Course Goals

The goal of this course is introduce the quantum mechanical concepts needed to understand the operation of current nanoelectronics and nanophotonics, as well as next-generation quantum information processing technologies. This course combines the use of course textbooks with current literature to show how quantum principles are used not simply to understand traditional physics applications but to understand new physical effects and their potential applications in transformative new technologies.

Students will be encouraged to work together to solve homework problems, and they should be prepared to individually communicate their understanding of course material.

Instructional Objectives

By the completion of 14 lectures (halfway mark), the students should have been introduced to the following and be able to do:

1. Understand Wave-Particle Duality and the wavefunction of a quantum system

2. Solve Schrödinger’s Equation in simple potentials

3. Fully analyze the behavior of a quantum harmonic oscillator

4. Understand the time-dependent Schrödinger Equation

5. Solve the time evolution of quantum wavepackets in various potentials

6. Compute expectation values and understand quantum operators

7. Explain the Uncertainty Principle and its applications

8. Understand the Hilbert space formalism of quantum mechanics

9. Perform calculations using bra-ket notation

10. Approximate solutions using first and second-order perturbation theory

11. Understand degenerate perturbation theory and the tight binding model

12. Understand time-dependent perturbation theory and Fermi’s Golden Rule

13. Compute the refractive index of a medium

14. Analyze the emergence of non-linear optical effects and their applications

By the end of the course (semester) students should be able to:

15. Work with angular momentum operators and spherical harmonics

16. Solve Schrödinger’s Equation for the hydrogen atom

17. Understand spin and the structure of qubits

18. Calculate the transmission coefficient in Resonant Tunneling

19. Explain Transmission Electron Microscopy

20. Understand LASERs

21. Analyze the scattering of identical particles

22. Understand the meaning of quantum entanglement and how it is detected

23. Explain the gate model of quantum computation

24. Identify universal sets of quantum gates

25. Construct basic quantum algorithms and compare with classical algorithms

26. Understand quantum teleportation and its use in processing quantum information

27. Explain the basic principles of quantum cryptography

Last updated

1/1/2019by Eric Chitambar