The Schrödinger Equation

absolutely continuous algebra analytic arbitrary asymptotics bounded commutes compact complete condition consider coordinates corresponding defined denote domain eigenfunctions eigenvalues eigenvectors energy operator equation estimate example exists finite follows formula Fourier transformation function H₁ H₂ Hence Hilbert space Hilbert-Schmidt Hilbert-Schmidt operator implies inequality isomorphism kernel L²(M L²(R L²(R+ Lebesgue measure Lemma Lie superalgebra linear mapping Math mathematical matrix multiplication operator norm Note obtain operator H orthogonal orthonormal particle path integral polynomial potential v(x proof of Theorem Proposition prove quantization quantum mechanics R₂ relations representation respect right-hand side satisfies scalar product Schrödinger operator self-adjoint operator solution space H spectral spectral theory spectrum subspace suffices supermanifold superspace t₁ Theorem 1.1 theory trace class uniquely unitary unitary operator variables vector verify wave operators Weyl symbol Wick symbol y₁(x zero