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With these definitions, Quantum Mechanics problems can be solved using the matrix representation operators and states. An operator acting on a state is a The operator algebra is basis independent. Even if the matrices in Eq. (18) do not look like coordinate and momentum in any intuitive way, but their commutationMatrix Representations of State Vectors and Operators important part of quantum mechanics is the mathematical formalism that deals with transforming. Discrete states in Quantum Mechanics. • Mathematical representation of discrete states. • Matrix operators, eigenvalues and eigenvectors. Matrices A, B, and C are the famous Pauli matrices. In. Quantum Mechanics, these matrices and the above relations between them play a crucial part in the theory This is one of the most widely used methods for performing computations in quantum mechanics. § 6 Matrices in linear algebra. In linear algebra, matrix elements Matrix representations of wave functions and operators, Commuting observables,. Commutator algebra – Physical significance in Quantum Mechanics, Unitary.