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- W3039694558 abstract "Complex-valued functions defined on a finite interval $[a,b]$ generalizing power functions of the type $(x-x_0)^n$ for $ngeq 0$ are studied. These functions called $Phi$-generalized powers, $Phi$ being a given nonzero complex-valued function on the interval, were considered to contruct a general solution representation of the Sturm-Liouville equation in terms of the spectral parameter cite{kravchenko2008, kravporter2010}. The $Phi$-generalized powers can be considered as a natural basis functions for the one-dimensional supersymmetric quantum mechanics systems taking $Phi=psi_0^2$, where the function $psi_0(x)$ is the ground state wave function of one of the supersymmetric scalar Hamiltonians. Several properties are obtained such as $Phi$-symmetric conjugate and antisymmetry of the $Phi$-generalized powers, a supersymmetric binomial identity for these functions, a supersymmetric Pythagorean elliptic (hyperbolic) identity involving four $Phi$-trigonometric ($Phi$-hyperbolic) functions as well as a supersymmetric Taylor series expressed in terms of the $Phi$-derivatives. We show that the first $n$ $Phi$-generalized powers are a fundamental set of solutions associated with a nonconstant coefficients homogeneous linear ordinary differential equations of order $n+1$. Finally, we present a general solution representation of the stationary Schrodinger equation in terms of geometric series where the Volterra compositions of the first type is considered." @default.
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- W3039694558 date "2020-07-01" @default.
- W3039694558 modified "2023-10-14" @default.
- W3039694558 title "Supersymmetric generalized power functions" @default.
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- W3039694558 doi "https://doi.org/10.1063/1.5144623" @default.
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