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The Mathematical Formulation of Quantum Mechanics
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Abelian absolutely continuous adjoint algebra analytic angular momentum asymptotic atom Banach space bounded operators calculation closed commute compact set complete concave constant continuous functions converges strongly defined Definition dense set domain eigenfunctions eigenvalues eigenvectors electrons equation equivalent essential spectrum essentially self-adjoint Example exists expectation value factor finite finite-dimensional follows formula Hamiltonian Hence Hermitian elements Hermitian operator Hilbert space implies inequality infinite infinity integral invariant kinetic energy limit lower bound mapping matrix measure norm orthogonal particles perturbation theory point spectrum positive potential Problem projection Proof properties proposition quantum mechanics quantum theory relative to H0 Remarks s-lim scattering Schrodinger self-adjoint extensions self-adjoint operator sequence Show singular Sp(a spectral representation spin strongly continuous subspace time-evolution topology transformation trial functions unitary upper bound vectors virial theorem wave-function weak topology weakly zero