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Linear Operators in Hilbert Spaces
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ansatz assume asymptotic Berry phase boundary condition bounded operators calculate called chapter commutator complex numbers conjugacy classes Consequently constants of integration convergence coordinates corresponding countable defined Definition delta function denotes differential equation Dirac discrete spectrum domain eigenfunctions eigenvalue equation eigenvalue problem eigenvectors elements energy equations of motion Example Find the eigenvalues finite follows form an orthonormal Fourier transform Hamilton function Hamilton operator harmonic oscillator Heisenberg Hilbert space infinite dimensional inverse Korteweg de Vries Kronecker product Lebesgue measure Let H linear operator linear space non-negative norm normalized notation obtain orthogonal orthonormal basis parameter phase polynomials potential pre-Hilbert space projection operator quantum mechanics real number Remark representation satisfied scalar product scattering Schrodinger equation self-adjoint operator set function space H spin matrices subset subspace takes the form tensor product term Theorem uncertainty relation underlying Hilbert space unit matrix unitary operator values vector wave function yields zero