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Using the orthonormality of the 2D-Zernike polynomials reproducing kernels, reproducing kernel Hilbert spaces and ensuing coherent states are attained. With the aid of the so obtained coherent states the complex unit disc is quantized. Associated upper symbols, lower symbols and related generalized ...
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A simple formula for computing the generalized Hubbell radiation rectangular source integralis introduced. Tables are given to compare the numerical values derived from our approximation formula with those given earlier in the literature.
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Infinite series, Sigma(n=1)(infinity) (alpha/2)(n)/n 1/n! F-1(1)(-n, gamma, x(2)), where F-1(1)(-n, gamma, x(2)) = n!/(gamma)(n) L-n((gamma-1))(x(2)), appear in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic oscillator Hamiltonian H = -d(2)/dx(2) + Bx...
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Infinite series of the type Sigma(n=1)(infinity)(alpha/2)n/n 1/n!F-2(1)(-n,b;gamma;y) are investigated. Closed-form sums are obtained for alpha a positive integer, alpha = 1, 2, 3,.... The limiting case of b --> infinity, after gamma is replaced with x(2)/b, leads to Sigma(n=1)(infinity)(alpha/2)...
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The asymptotic iteration method is used to find exact and approximate solutions of Schrödinger’s equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent). Analytic and approximate solutions are obtained by first using ...
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The one-dimensional Schr ̈odinger’s equation is analysed w ith regard to the existence of exact solutions for decatic polynomial potentials. Under c ertain conditions on the potential’s pa- rameters, we show that the decatic polynomial potential V ( x ) = ax 10 + bx 8 + cx 6 + dx 4 + ex 2 , a >...
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