Lectures in Mathematical Physics, Volume 2 |
Contents
Introduction to Quantum Mechanics | 1 |
An Existence and Uniqueness Theorem for Linear | 6 |
Chapter II | 81 |
Copyright | |
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A₁ A₂ algebra structure classical mechanics commutator compact complex numbers complex vector space connected convergence curve defined DEFINITION denote DGCV differential equation Dirac direct sum eigenvalues eigenvectors elements of G EXERCISE exp(tA ɛ G f₁ finite dimensional formula Fourier transform function f hence Hermitian operators Hilbert space homomorphism inner product integral invariant irreducible representations isomorphic lemma Let G Lie algebra Lie group linear transformations m₁ m₂ mathematical matrix measure metric space notation one-parameter group one-parameter subgroup operators on H orthogonal orthonormal basis particle physicists physics Poisson bracket Proof prove quantum mechanics quotient real numbers real vector space relation representation of G right hand side satisfies Schrödinger Section solution space H subalgebra subgroup of G subset subspace symmetric tation THEOREM theory tion topological topological group trace unitary operators V₁ V₂ X₁ ψε