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Master Course Description for, Schemes and Mind Maps of Quantum Mechanics

Notre Dame College (NDC)Quantum Mechanics

Goals: The focus of this course is to introduce students to quantum mechanics using 1D, 2D and. 3D nanomaterials. The students will develop a working ...

Typology: Schemes and Mind Maps

2022/2023

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Master Course Description for
No: EE 421
Title: QUANTUM MECHANICS FOR ENGINEERS
Credits: 3/4 (3/4 lecture)
Coordinator: M.P. Anantram, Professor, Electrical Engineering
Goals: 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, nanomaterials,
basics of quantum information.
Learning Objectives:
At the end of the course, the student should be able to:
1) Understand how to interpret wave function
2) Solve Schrodinger’s wave equation
3) Calculate basic expressions for tunneling through barriers and resonant tunneling
phenomena
4) Solve Schrodinger’s equation numerically at the level of a typical experimentalist
5) Calculate the role of quantization in technological relevant examples: quantum dots,
nanowires, quantum wells
6) Interpret De Broglie’s Uncertainity Principle and Energy-Time Uncertainity Principle
7) Learn method of separation of variables
8) Learn basics of the tight binding method and apply to examples
9) Apply Bloch’s theorem in bulk and nanomaterials to calculate the bandstructure
10) Calculate Density of states of closed and extended systems
11) Learn about the basics of spins and representation of logic states using spins
12) Derive and apply Fermi’s golden rule for transition rates. Examples include electron-
photon interaction / optical absorption / electron-impurity scattering
Textbook: No text is required for the course. Professor will upload typewritten notes and other
material on to course website.
Supplemental and Reference Materials:
1) Quantum Mechanics: For Engineering, Materials Science, and Applied Physics: 1st
Edition (3/7/1994) by Herbert Kroemer, Publisher: Prentice Hall (Book for general
quantum mechanics)
2) Quantum Transport: Atom to Transistor: 1st Edition (6/30/2005) by Supriyo Datta,
Publisher: Cambridge University Press (For tight binding)
Prerequisites: MATH 307 or AMATH 351
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Master Course Description for

No: EE 421

Title: QUANTUM MECHANICS FOR ENGINEERS

Credits: 3/4 (3/4 lecture)

Coordinator: M.P. Anantram, Professor, Electrical Engineering

Goals: 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, nanomaterials, basics of quantum information.

Learning Objectives:

At the end of the course, the student should be able to:

  1. Understand how to interpret wave function
  2. Solve Schrodinger’s wave equation
  3. Calculate basic expressions for tunneling through barriers and resonant tunneling phenomena
  4. Solve Schrodinger’s equation numerically at the level of a typical experimentalist
  5. Calculate the role of quantization in technological relevant examples: quantum dots, nanowires, quantum wells
  6. Interpret De Broglie’s Uncertainity Principle and Energy-Time Uncertainity Principle
  7. Learn method of separation of variables
  8. Learn basics of the tight binding method and apply to examples
  9. Apply Bloch’s theorem in bulk and nanomaterials to calculate the bandstructure
  10. Calculate Density of states of closed and extended systems
  11. Learn about the basics of spins and representation of logic states using spins
  12. Derive and apply Fermi’s golden rule for transition rates. Examples include electron- photon interaction / optical absorption / electron-impurity scattering

Textbook: No text is required for the course. Professor will upload typewritten notes and other material on to course website.

Supplemental and Reference Materials:

  1. Quantum Mechanics: For Engineering, Materials Science, and Applied Physics : 1st Edition (3/7/1994) by Herbert Kroemer, Publisher: Prentice Hall (Book for general quantum mechanics)
  2. Quantum Transport: Atom to Transistor : 1st Edition (6/30/2005) by Supriyo Datta, Publisher: Cambridge University Press (For tight binding)

Prerequisites: MATH 307 or AMATH 351

Topics:

  1. Schrodinger’s eqn a. Definition b. Interpretation c. Continuity equation for probability density d. Continuity of wave function and its first derivative e. Expectation value f. Uncertainty principle

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

a. Particle in a box b. Single Barrier Tunneling (discussion in context of transistors) c. Double Barriers (resonant tunneling diodes) d. Separation of variables e. Nanowire f. Quantum Well g. Quantum Dot h. Hydrogen Atom i. Kronig-Penney model* j. Time evolution of wave packets

  1. Crystalline solid

a. Unit cell and Basis vectors b. Real space and Reciprocal space c. Bloch’s theorem (Energy levels, wave function) i. Carbon nanotubes ii. Graphene iii. Diamond

  1. Density of states of open and closed systems

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

  1. Spins

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

  1. Fundamentals of quantum information concepts

a. Entanglement b. Gates c. Quantum Computing (example)

(g) (H) An ability to communicate effectively. The students will develop an ability to explain their rationale for assumptions and approximation made in solving engineering problems. This will occur in homework, where the students will be graded for communicating the motivation behind engineering/physical assumptions and approximations and the resulting mathematical assumptions.

(h) The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental and societal context. (N/A)

(i) (M) A recognition of the need for and an ability to engage in life-long learning. The course will provide a working knowledge of many quantum concepts for students but cannot be considered comprehensive. The fundamentals learnt in the course will provide a basis for the students to engage in further formal/informal study of emerging quantum technologies.

(j) (H) Knowledge of contemporary issues. The course is designed around emerging and existing engineering application involving quantum confined nanomaterials.

(k) (L) An ability to use the techniques, skills and modern engineering tools necessary for engineering practice. The student’s will use mathematical / computational tools that are freely available to UW students to perform design and analysis.

Prepared By: Anant M.P. Anantram, 10/28/