Hamiltonian structure

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31: 18.2 General Orthogonal Polynomials

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Degree lowering and raising differentiation formulas and structure relations

… ►Then the OP’s are called semi-classical and (18.2.44) is called a structure relation. …

32: 3.11 Approximation Techniques

… ►The method of the fast Fourier transform (FFT) exploits the structure of the matrix $𝛀$ with elements ${\omega }_n^{jk}$, $j,k=0,1,\mathrm{\dots },n-1$. …In consequence of this structure the number of operations can be reduced to $nm=n{\log }_{2}n$ operations. …

33: 3.8 Nonlinear Equations

… ►For an arbitrary starting point $z_0\in ℂ$, convergence cannot be predicted, and the boundary of the set of points $z_0$ that generate a sequence converging to a particular zero has a very complicated structure. …

34: Bibliography S

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Structure of avoided crossings for eigenvalues related to equations of Heun’s class. J. Phys. A 30 (2), pp. 673–687.

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ISSN 0305-4470, Document, MathReview (Éric Delabaere), ZentralBlatt

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§31.13.

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35: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►The sum of the kinetic and potential energies give the quantum Hamiltonian, or energy operator; often also referred to as a Schrödinger operator. …