By application of the coinduction method as well as Magri method to the ideal of real Hilbert-Schmidt operators we construct the hierarchies of integrable Hamiltonian systems on the Banach Lie-Poisson spaces which consist of these type of operators. We also discuss their algebraic and analytic properties as well as solve them in dimensions N = 2, 3, 4.
Solutions of the q-deformed Schrödinger equation are presented for the following potentials: shifted oscillator, isotropic oscillator, Rosen–Morse II, Eckart II, and Poschl–Teller I and II potentials. Various properties of solutions to such equations are discussed including the limit case q → 1 that corresponds to the non-deformed Schrödinger equation.
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