منابع مشابه
Exact solutions for a family of discretely spiked harmonic oscillators
5 Normalization and orthogonalization 15 5.1 Admissible physical solutions . . . . . . . . . . . . . . . . . . 16 5.2 Linear normalization . . . . . . . . . . . . . . . . . . . . . . . 16 5.3 Radial normalization . . . . . . . . . . . . . . . . . . . . . . . 18 5.3.1 One dimensional . . . . . . . . . . . . . . . . . . . . . 18 5.3.2 Two dimensional . . . . . . . . . . . . . . . . . . . . . 20 5...
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...
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New equations are proposed for frequency and amplitude of a ring oscillator. The method is general enough to be used for all types of delay stages. Using exact largesignal circuit analysis, closed form equations for estimating the frequency and amplitude of a high frequency ring oscillator are derived as an example. The method takes into account the effect of various parasitic capacitors to...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2010
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/43/38/385302