MATH-495: Mathematical quantum mechanics

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Lectures in this course (30)

Herglotz Representation Theorem

Covers the Herglotz representation theorem and the construction of projection-valued measure.

Quantum Measurement Postulate

Explores the verification of PVM properties and the spectral theorem for unbounded operators in quantum mechanics.

Quantum Mechanics: Spectral Basis and Schrödinger Equation

Explores spectral basis, Schrödinger equation, unitary equivalence, and self-adjoint operators.

Unitary Group and Spectral Types

Covers the proof of unitary group uniqueness and spectral types.

Quantum Dynamics: Spectral Decomposition

Explores the spectral decomposition of Hilbert space and its implications in quantum dynamics.

Compact Operators: Properties and Theorems

Covers properties and theorems related to compact and relatively compact operators, including the RAGE theorem and the Kato-Rellich theorem.

Stability of Atoms

Explores the stability of atoms in quantum mechanics, emphasizing the Coulomb uncertainty principle and its impact on electron behavior within the nucleus.

Hydrogenic Atom Stability

Covers the proof of the Coulomb uncertainty principle and the stability of hydrogenic atoms.

Proof of Weyl's Theorem

Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.

Ground State Energy: Harmonic Oscillator and Perturbation

Covers the ground state and energy of harmonic oscillators and perturbations by bounded potentials.

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