Generalized Schwinger duality in bound state theory

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Abstract
It is shown that an exactly solvable bound state problem is the generator of a nonterminable sequence of partially exactly solvable problems. The reversible passage from exact to partial solvability is realized through a class of admissible nonlinear coordinate transformations of which the parabolic Schwinger transformation that relates the Coulomb and oscillator problems is a particular case. Interesting spectral features of a novel set of partially solvable problems that emerge through the present considerations are also pointed out.