ECE 487

• Microelectronics and Photonics

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.)

• 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

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 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

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

Engineering Science: 3 credits

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.

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 (1,6)

2. Solve Schrödinger’s Equation in simple potentials (1,5,6)

3. Fully analyze the behavior of a quantum harmonic oscillator (1,6)

4. Understand the time-dependent Schrödinger Equation (1,6)

5. Solve the time evolution of quantum wavepackets in various potentials (1,5,6)

6. Compute expectation values and understand quantum operators (1,6)

7. Explain the Uncertainty Principle and its applications (3,7)

8. Understand the Hilbert space formalism of quantum mechanics (1,6)

9. Perform calculations using bra-ket notation (1,6)

10. Approximate solutions using first and second-order perturbation theory (1,6)

11. Understand degenerate perturbation theory and the tight binding model (1,6)

12. Understand time-dependent perturbation theory and Fermi’s Golden Rule (1,6)

13. Compute the refractive index of a medium (1,6)

14. Analyze the emergence of non-linear optical effects and their applications (1,6)

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

15. Work with angular momentum operators and spherical harmonics (1)

16. Solve Schrödinger’s Equation for the hydrogen atom (1,5,6)

17. Understand spin and the structure of qubits (1,6)

18. Calculate the transmission coefficient in Resonant Tunneling (1,6)

19. Explain Transmission Electron Microscopy (3,7)

20. Understand LASERs (1,6)

21. Analyze the scattering of identical particles (1,6)

22. Understand the meaning of quantum entanglement and how it is detected (1,6)

23. Explain the gate model of quantum computation (3,7)

24. Identify universal sets of quantum gates (1,6)

25. Construct basic quantum algorithms and compare with classical algorithms (1,5,6)

26. Understand quantum teleportation and its use in processing quantum information (1,6)

27. Explain the basic principles of quantum cryptography (3,7)