one-dimensional
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1—10 of 11 matching pages
1: 15.18 Physical Applications
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►The hypergeometric function has allowed the development of “solvable” models for one-dimensional quantum scattering through and over barriers (Eckart (1930), Bhattacharjie and Sudarshan (1962)), and generalized to include position-dependent effective masses (Dekar et al. (1999)).
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2: 36.15 Methods of Computation
3: 12.17 Physical Applications
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►Dean (1966) describes the role of PCFs in quantum mechanical systems closely related to the one-dimensional harmonic oscillator.
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4: 18.39 Applications in the Physical Sciences
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Introduction and One-Dimensional (1D) Systems
►The fundamental quantum Schrödinger operator, also called the Hamiltonian, , is a second order differential operator of the form … ►These eigenfunctions are the orthonormal eigenfunctions of the time-independent Schrödinger equation …which in one dimensional systems are typically non-degenerate, namely there is only a single eigenfunction corresponding to each , . … ►1D Quantum Systems with Analytically Known Stationary States
…5: 20.11 Generalizations and Analogs
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►For specialization to the one-dimensional theta functions treated in the present chapter, see Rauch and Lebowitz (1973) and §21.7(iii).
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6: Bibliography F
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Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice.
Phys. A 190 (3-4), pp. 346–362.
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7: Bibliography D
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Unification of one-dimensional Fokker-Planck equations beyond hypergeometrics: Factorizer solution method and eigenvalue schemes.
Phys. Rev. E (3) 57 (1), pp. 252–275.
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8: 18.38 Mathematical Applications
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►Light and Carrington Jr. (2000) review and extend the one-dimensional analysis to solution of multi-dimensional many-particle systems, where the sparse nature of the resulting matrices is highly advantageous.
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9: Bibliography C
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Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity.
Phys. Rev. A 62 (063610), pp. 1–10.
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10: Bibliography S
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Asymptotic Solutions of the One-dimensional Schrödinger Equation.
American Mathematical Society, Providence, RI.
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