منابع مشابه
Generalized Spiked Harmonic Oscillator
A variational and perturbative treatment is provided for a family of generalized spiked harmonic oscillator Hamiltonians H = − d dx + Bx + A x + λ xα ,where B > 0, A ≥ 0 , and α and λ denote two real positive parameters. The method makes use of the function space spanned by the solutions |n> of Schrödinger’s equation for the potential V (x) = Bx + A x . Compact closed-form expressions are obtai...
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A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator − d dx2 +Bx+ A x2 + λ x , where α is a real positive parameter. The formalism makes use of a basis provided by exact solutions of Schrödinger’s equation for the Gol’dman and Krivchenkov Hamiltonian, and the corresponding matrix elements that were previously found. For all the discrete eigenva...
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Quantum particle is assumed located in an analytically perturbed harmonic-oscillator potential. Its motion along certain complex, PT −symmetric “toboggan” paths which N−times encircle the branch point in the origin is studied in both the boundstate and scattering regime.
متن کاملSpiked Harmonic Oscillators
A complete variational treatment is provided for a family of spiked-harmonic oscillator Hamiltonians H = − d dx2 + Bx + λ x (B > 0, λ > 0 ), for arbitrary α > 0 . A compact topological proof is presented that the set S = {ψn} of known exact solutions for α = 2 constitutes an orthonormal basis of the Hilbert space L2(0,∞) . Closed-form expressions are derived for the matrix elements of H with re...
متن کاملPerturbation expansions for the spiked harmonic oscillator and related series involving the gamma function
We study weak-coupling perturbation expansions for the ground-state energy of the Hamiltonian with the generalized spiked harmonic oscillator potential V (x) = Bx + A x + λ x , and also for the bottoms of the angular momentum subspaces labelled by l = 0, 1, . . . , in N -dimensions corresponding to the spiked harmonic oscillator potential V (x) = x + λ x , where α is a real positive parameter. ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2001
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/34/6/308