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Introduction to Quantum Mechanics
Dirac Spaces and Generalized
Groups and Their Represen
32 other sections not shown
algebra structure ators automorphism classical mechanics commutator compact complex numbers complex vector space condition connected convergence curve defined DEFINITION denote DGCV differential equation Dirac direct sum eigenvalues eigenvectors elements of G EXERCISE finite dimensional formula Fourier transform function f g e G GL(n hence Hermitian operators Hilbert space homomorphism inner product integral invariant irreducible representations isomorphic lemma Let G Lie algebra Lie group linear transformations Lorentz mathematical measure metric space n x n notation observables one-parameter group one-parameter subgroup operators on H orthogonal orthonormal basis particle physicists physics Poisson bracket Proof prove quantum mechanics quotient rapidly decreasing real numbers real vector space relation representation of G right hand side satisfies Schrodinger Section solution space H subalgebra subgroup of G subset subspace Suppose G symmetric tation THEOREM tion topological group trace unitary operators zero