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Introduction to Quantum Mechanics
Dirac Spaces and Generalized
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adjoint algebra structure ators automorphism classical mechanics commutator compact complex numbers complex vector space connected convergence curve defined DEFINITION denote differential equation dimension direct sum eigenvalues eigenvectors elements of G EXERCISE finite dimensional formula Fourier transform g e G GL(n hence Hermitian operators Hilbert space homomorphism inner product integral irreducible representations isomorphic lemma Let G Lie algebra Lie group linear transformations mathematical matrix elements metric space multiple 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 scalars Schrodinger Section skew-Hermitian operators solution space H subalgebra subgroup of G subset subspace Suppose G symmetric tation THEOREM tion topological group trace unitary operators variables zero