difference%20operators
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4 matching pages ♦
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4 matching pages
1: Bibliography D
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Computing spectra of linear operators using the Floquet-Fourier-Hill method.
J. Comput. Phys. 219 (1), pp. 296–321.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Linear operators. Part II.
Wiley Classics Library, John Wiley & Sons, Inc., New York.
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Differential-difference operators associated to reflection groups.
Trans. Amer. Math. Soc. 311 (1), pp. 167–183.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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2: Bibliography K
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Connecting Jacobi elliptic functions with different modulus parameters.
Pramana 63 (5), pp. 921–936.
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Lowering and Raising Operators for Some Special Orthogonal Polynomials.
In Jack, Hall-Littlewood and Macdonald Polynomials,
Contemp. Math., Vol. 417, pp. 227–238.
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Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators.
SIGMA Symmetry Integrability Geom. Methods Appl. 11, pp. Paper 074, 22.
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Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator.
Adv. Math. 333, pp. 796–821.
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Algorithm 910: a portable C++ multiple-precision system for special-function calculations.
ACM Trans. Math. Software 37 (4), pp. Art. 45, 27.
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3: 14.30 Spherical and Spheroidal Harmonics
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►Sometimes is denoted by ; also the definition of can differ from (14.30.1), for example, by inclusion of a factor .
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Parity Operation
… ►Here, in spherical coordinates, is the squared angular momentum operator: …and is the component of the angular momentum operator ►
14.30.13
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4: 18.39 Applications in the Physical Sciences
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►The fundamental quantum Schrödinger operator, also called the Hamiltonian, , is a second order differential operator of the form
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►Analogous to (18.39.7) the 3D Schrödinger operator is
…where is the (squared) angular momentum operator (14.30.12).
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►Here tridiagonal representations of simple Schrödinger operators play a similar role.
The radial operator (18.39.28)
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