A two-parameter family of nonlinear coherent states is defined for the pseudoharmonic oscillator by generalizing the factorial in the expansion coefficients, with conditions ensuring normalization and resolution of the identity.
Spiked harmonic oscillators
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abstract
A complete variational treatment is provided for a family of spiked-harmonic oscillator Hamiltonians H = -d^2/dx^2 + B x^2 + lambda/x^alpha, B > 0, lambda > 0, for arbitrary alpha > 0. A compact topological proof is presented that the set S = {psi_n} of known exact solutions for alpha = 2 constitutes an orthonormal basis for the Hilbert space L_2(0, infinity). 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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math-ph 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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A set of nonlinear coherent states for the pseudoharmonic oscillator
A two-parameter family of nonlinear coherent states is defined for the pseudoharmonic oscillator by generalizing the factorial in the expansion coefficients, with conditions ensuring normalization and resolution of the identity.