01 / Foundations
Postulates of quantum mechanics
Core assumptions for states, observables, measurements, time evolution, and quantization.
Open noteOpen teaching notes
Quantum Mechanics notes
These notes are arranged as a learning path through the mathematical language of quantum mechanics: postulates, expectation values, continuous spectra, symmetry generators, operator representations, time evolution, and uncertainty.
Learning path
Suggested order
The order below follows the dependencies among the notes, starting from the postulates and ending with uncertainty relations as a synthesis of expectations, operators, and commutators.
02 / Measurement averages
Expectation values
How quantum states encode average measurement outcomes and statistical information.
Open note03 / Continuous bases
Operators with continuous spectra
Position-like observables, probability densities, and eigenstate expansions beyond discrete bases.
Open note04 / Symmetry and generators
Generators and transformations
How infinitesimal transformations connect operators, symmetry, and physical change.
Open note05 / Operator representation
Position and momentum operators
Operator representations in position space and their connection to wavefunctions.
Open note06 / Time evolution
Schrodinger equation
Time evolution, unitary dynamics, and the Hamiltonian as the generator of quantum motion.
Open note07 / Statistical structure
The uncertainty principle
The operator and statistical structure behind uncertainty relations.
Open noteCourse context
Working teaching materials
The notes are shared as working materials from the undergraduate Quantum Mechanics course. They are most useful alongside lectures, problem solving, and discussion.
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