Quantum Mechanics

Quantum mechanics is the latest physical theory that most accurately describes the natural world. A key understanding of quantum mechanics is crucial to a deep grasp of quantum computing.

Topics(each topic takes 2~3 weeks)

1. Linear Algebra

   • Textbook

     1. Vectors: Appendix A.1

     2. Inner Products: Appendix A.2

     3. Matrices: Appendix A.3

     4. Bases Transformations: Appendix A.4

     5. Eigenvectors and Eigenvalues: Appendix A.5

     6. Hermitian Transformations: Appendix A.6

   • Lectures:

     1. Introduction to Quantum Computing and Quantum Information(Taehyun, Kim, SNU): Lectures 1~6

2. Schrodinger Equation

   • Textbook:

     1. Introduction to the wave function and Schrodinger equation: Section 1.1~Section 1.5

     2. Time Independent Schrodinger Equation

        1. Stationary States: Section 2.1

        2. Infinite Square Well: Section 2.2

        3. Harmonic Oscailltor: Section 2.3

        4. Free Particle: Section 2.4

        5. Delta Function Potential: Section 2.5

        6. Finite Square Well: Section 2.6

   • Lectures: MIT Quantum Physics 1

     1. An overview of quantum mechanics: L1.1~L2.5

     2. Momentum operator, Schrödinger equation, and interpretation of the wavefunction: L 5.1~ L5.5

     3. Probability density and current. Hermitian conjugation: L 6.1~L6.4

     4. Infinite Square Well: L 11.2~ L 11.3

     5. Finite Square Well: L 11.4~ L 11.5

     6. Delta Function Potential: L 13.1~ L 13.2

     7. Harmonic Oscillator: L 13.4~L 15.3

3. Formalism

   • Textbook:

     1. Hilbert Space: Section 3.1

     2. Observables: Section 3.2

     3. Eigenfunctions of a Hermitian Operator: Section 3.3

     4. Uncertainty Principle: Section 3.5

     5. Vectors and Operators: Section 3.6

   • Lectures: MIT Quantum Physics 1

     1. Expectation values of operators: L 8.4

     2. Time dependence of expectation values: L 8.5

     3. Observables, Hermitian operators, measurement and uncertainty. Particle on a circle: L 9.1~ L 9.5

4. Spin, Angular Momentum, Two Particle Systems

   • Textbook:

     1. Quantum Angular Momentum Operator: Section 4.3

     2. Spin: Section 4.4

     3. Two-Particle Systems(Fermions, Bosons): Section 5.1

   • Lectures: MIT Quantum Physics 1

     1. Angular Momentum: L 20.2~L 20.4

5. Conservation Laws, and the Variational Principle

   • Textbook:

     1. Variational Principle: Section 8.1 

     2. Intro to operator transformations: Section 6.1 

     3. Translation Operator: Section 6.2

     4. Conservation Laws: Section 6.3

     5. Rotational Symmetry: Section 6.5

     6. Degeneracy: Section 6.6

     7. Translations in time: Section 6.8

6. EPR, No-Clone Theorem, Bell's Theorem, Density Matrix and Mixed States

   • Textbook:

     1. EPR Paradox & Bell's Theorem: Section 12.1~12.2

     2. Density Matrix and Mixed States: Section 12.3

     3. The no-clone theorem: Section 12.4