PH 425 (Quantum Fundamentals) Math Bits

Unit: Matrices

Matrix Manipulations (45 minutes)

Unit: Complex Numbers

Algebra of Complex Numbers (50 minutes)

Unit: Operators and Transformations in Linear Systems

Introduction to Bra-ket notation (15 minutes)

Linear Transformations (1 1/2 hr)

Unit: Vector Spaces

Tangible Metaphor for Complex Vectors (10 minutes)

Properties of Linear Vector Spaces (20 min)

Inner Products and Norms

  • Calculating Inner Products and Normalization of Vectors (Lecture, 10 minutes)

FIXME Write these lecture notes. Emphasize complex vectors.

Matrix Components (30 min)

Note: This activity can be done as a homework problem.

Rotation Matrices in 2 and 3 Dimensions (10 min--optional)

Unit: Eigenvalues and Eigenvectors

Eigenvalues & Eigenvectors (2 hr)

Unit: Special Matrices

Note: At OSU in Paradigms 2.0, work this content into the Spins course as needed.

Special Properties of Hermitian Matrices (40 min)

Commuting Matrices (10 min)

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