Quantum Formalism
PHYS 410 · Module 4
This module develops the abstract mathematical framework of quantum mechanics. Students study Hilbert spaces, operators, eigenvalues, expectation values, and Dirac notation.
Lessons in this module
Hilbert space and state vectors
Quantum states live in Hilbert space, a complex vector space with an inner product. This lesson connects wavefunctions, vectors, bases, superposition, and normalization.
Operators and observables
Quantum observables are represented by operators acting on states. This lesson explains linear operators, Hermitian operators, commutators, compatible observables, and measurement.
Eigenvalues and expectation values
Eigenvalues are possible measurement results, while expectation values are statistical averages. This lesson explains spectra, probability distributions, variance, and repeated measurements.
Dirac notation
Dirac notation provides a compact language for quantum states, inner products, operators, and basis expansions. This lesson explains kets, bras, projectors, and completeness.
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