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Matrix mechanics is the matrix-based formulation of quantum mechanics developed by Heisenberg, Born, and Jordan, and books in this category present quantum theory through linear algebra and operator methods. They treat states and observables as vectors and matrices, emphasize noncommuting operators and commutation relations, and develop core ideas such as the uncertainty principle, eigenvalues/eigenvectors and spectra, time evolution, and transition amplitudes. Typical treatments cover the harmonic oscillator, angular momentum and spin, selection rules, and symmetries, often alongside comparisons with Schrödinger’s wave mechanics and demonstrations of their equivalence within the modern Hilbert-space framework. The category includes textbooks, problem collections, monographs, and historical accounts, with applications to atomic, molecular, nuclear, and condensed-matter physics. It is generally aimed at advanced undergraduates, graduate students, and researchers with a background in calculus and linear algebra.

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