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Article Transmission Eigenvalues Problem of a Schrödinger Equation(Tubitak Scientific & Technological Research Council Turkey, 2024) Yıldırım, Emel; Baıramov, ElgizIn this paper, transmission eigenvalues of a Schrödinger equation have been studied by constructing a new inner product and using Weyl theory. Necessary conditions for these eigenvalues to be negative, real, and finite have been examined. This method has provided a new framework related to transmission eigenvalue problems and the investigation of their properties. The conclusions have been verified for the special case of the problem.Article Spectrum of a Q-Deformed Schrödinger Equation by Means of the Variational Method(Wiley, 2023) Calisir, Ayse Dogan; Turan, Mehmet; Adiguzel, Rezan SevinikIn this work, the q-deformed Schr & ouml;dinger equations defined in different form of the q-Hamiltonian for q-harmonic oscillator are considered with symmetric, asymmetric, and non-polynomial potentials. The spectrum of the q-Hamiltonian is obtained by using the Rayleigh-Ritz variational method in which the discrete q-Hermite I polynomials are taken as the basis. As applications, q-harmonic, purely q-quartic, and q-quartic oscillators are examined in the class of symmetric polynomial potentials. Moreover, the q-version of Gaussian potential for an example of a non-polynomial symmetric potential and a specific example of q-version of asymmetric double well potential are presented. Numerous results are given for these potentials for several values of q. The limit relation as q ? 1(-) is discussed. The obtained results of ground-and excited-state energies of the purely q-quartic oscillator and the accuracy of the ground-state energy levels are compared with the existing results. Also, the results are compared with the classical case appearing in the literature in the limiting case q?1(-).
