Spiked Harmonic Oscillators
نویسندگان
چکیده
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 respect to S . These analytical results, and the inclusion of a further free parameter, facilitate optimized variational estimation of the eigenvalues of H to high accuracy.
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تاریخ انتشار 2002