Sobolev Spaces and Unitary Groups

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Unitary Group and Spectral Types

Covers the proof of unitary group uniqueness and spectral types.

Position and Momentum Operators

Explores position and momentum operators, eigenstates, and probability density in three dimensions.

Real Numbers: Sets and Operations

Explores the fundamental concepts of real numbers, including sets, operations, and properties like supremum and infimum.

Translation Groups on [0,1]

Covers the study of translation groups on the interval [0,1] with different phases and the Riesz representation theorem on Hilbert space.

Cohomology Real Projective Space

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Dynamics of Solid Bodies

Explores the dynamics of solid bodies, covering speed, acceleration, and rotation principles.

Advanced Physics I: Orders of Magnitude

Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.

Rotation Dynamics: Symmetry Axis

Explores rotation dynamics around a symmetry axis, covering angular momentum, center of mass theorem, and solid body movement.

Sobolev Spaces in Higher Dimensions

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Quantum Harmonic Oscillator: Basics and Operators

Introduces the quantum harmonic oscillator basics, including operators and energy states.