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The pseudoperturbative shifted-l expansion technique is introduced to determine nodeless states of the 2D Schrodinger equation with arbitrary cylindrically symmetric potentials. Exact energy eigenvalues and eigenfunctions for the 2D Coulomb and harmonic oscillator potentials are reproduced. Moreover, exact energy eigenvalues, compared with those obtained by numerical solution (V.M. Villalba and R. Pino, J. Phys.: Condens. Matter 8 (1996) 80671, were obtained for the hybrid of the 20 Coulomli and oscillator potentials.

2D H-Atom in an Arbitrary Magnetic Field via Pseudoperturbation Expansions Through the Quantum Number l