Abstract
We construct two-dimensional integrable and superintegrable systems in terms of the master function formalism and relate them to Mielnik’s and Marquette’s construction in supersymmetric quantum mechanics. For two different cases of the master functions, we obtain two different two-dimensional superintegrable systems with higher order integrals of motion.
Highlights
It is known from classical and quantum mechanics that a system with N degrees of freedom is called completely integrable if it allows N functionally independent constants of the motion [1]
From the mathematical and physical point of view, these systems play a fundamental role in description of physical systems due to their many interesting properties
For a quantum superintegrable system, one should define another operator such as A2 which commutates with the Hamiltonian of system, that is, [H, A2] = 0, but [A1, A2] ≠ 0
Summary
It is known from classical and quantum mechanics that a system with N degrees of freedom is called completely integrable if it allows N functionally independent constants of the motion [1]. X-axis and its he has obtained a two-dimensional superintegrable system as Hs = Hx + Hy, which can be separated in Cartesian coordinates with creation and annihilation operators a+(x), a−(x), s+(y), and s−(y) He has shown that the Hamiltonian Hs possesses the following integrals of motion:. In [19, 20], the authors have shown that the second-order differential equations and their associated differential equations in mathematical physics have the shape invariant property of supersymmetry quantum mechanics They have shown that by using a polynomial of a degree not exceeding two, called the master function, the associated differential equations can be factorized into the product of rising and lowering operators.
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