The path integral evaluation of the hydrogen atom by Duru and Kleinert is studied by recognizing it as a special case of the general treatment of the separable Hamiltonian of Liouville-type. The basic dynamical principle involved is identified as the Jacobi’s principle of least action for given energy which is reparametrization invariant, and thus the appearance of a gauge freedom is naturally ...

In this study, fractional differential transform method (FDTM), which is a semi analytical-numerical technique, is used for computing the eigenelements of the Sturm-Liouville problems of fractional order. The fractional derivatives are described in the Caputo sense. Three problems are solved by the present method. The calculated results are compared closely with the results obtained by some exi...

The problem of constructing semi-discrete integrable analogues the Liouville type PDE is discussed. We call equation a discretization if these two equations have common integral. For from well-known Goursat list for which integrals minimal order are less than or equal to we presented corresponding versions. contains new examples non-autonomous Darboux chains.

In this paper we obtain unstable even-parity eigenmodes to the static regular spherically symmetric solutions of the SU(2) Yang-Mills-dilaton coupled system of equations in 3+1 Minkowski space-time. The corresponding matrix Sturm-Liouville problem is solved numerically by means of the continuous analogue of Newton's method. The method, being the powerful tool for solving both boundary-value and...

In this paper, we study q-Sturm-Liouville operators. We construct a space of boundary values of the minimal operator and describe all maximal dissipative, maximal accretive, self-adjoint and other extensions of q-Sturm-Liouville operators in terms of boundary conditions. Then we prove a theorem on completeness of the system of eigenfunctions and associated functions of dissipative operators by ...