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We apply the Schr\"odinger factorization to construct the ladder operatorsfor hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonicoscillator in arbitrary dimensions. By generalizing these operators we showthat the dynamical algebra for these problems is the $su(1,1)$ Lie algebra.

journal of physics. a, mathematical and theoretical

The su(1,1) dynamical algebra from the Schr\"odinger ladder operators  for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic  oscillator and pseudo-harmonic oscillator