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math-ph2003★ 1 cited
Friedrichs extensions of Schroedinger operators with singular potentials
Attila B. von Keviczky, Nasser Saad, Richard L. Hall
The Friedrichs extension for the generalized spiked harmonic oscillator given by the singular differential operator -D^2+ Bx^2 + Ax^{-2} + lambda x^{-alpha} (B>0, A >= 0) in L_2(0,…
math-ph2002
Generalized comparison theorems in quantum mechanics
Richard L. Hall, Qutaibeh D. Katatbeh
This paper is concerned with the discrete spectra of Schroedinger operators H = -Delta + V, where V(r) is an attractive potential in N spatial dimensions. Two principal results are…
math-ph2000
Smooth spectral transition from Coulomb to oscillator
Richard L. Hall
Non-relativistic potential models are considered of the pure power V(r) = sgn(q) r^q and logarithmic V(r) = ln(r) types. Envelope representations and kinetic potentials are employe…