Abstract The solution to the one dimensional Schrodinger equation for the potential of type x 2 + αx −2, for positive values of the constant α is discussed using an operator method by factorizing the Hamiltonian.
Abstract In this work, we find the exact solution of Schrödinger wave equation for position dependent mass with pseudoharmonic oscillator using extended Nikiforov-Uvarov method. We obtained the energy-eigen equation presented in a closed and compact form and used the result to study both superstatistics and thermodynamic properties by first determining the partition function of the system. The unnormalized wave function was obtained and expressed in terms of Confluent Heun function. Using the resulting energy eigen equation, the numerical computation were computed for varying masses for with fixed physical constant potential parameter λ. The numerical result shows that the bound state energies increase with quantum states but decreases with the dependent mass m(x). The thermodynamics and superstatistics plots are also reported.
PT symmetric Hamiltonian model and Dirac equation in 1+1 dimensions
In this paper, we have introduced a symmetric non-Hermitian Hamiltonian model which is given as where ω and α are real constants, and are first-order differential operators. The Hermitian form of the Hamiltonian is obtained by suitable mappings and it is interrelated to the time-independent one-dimensional Dirac equation in the presence of position-dependent mass. Then, Dirac equation is reduced to a Schrödinger-like equation and two new complex non- symmetric vector potentials are generated. We have obtained a real spectrum for these new complex vector potentials using the shape invariance method. We have searched the real energy values using numerical methods for the specific values of the parameters.
In this work, the quantum operator approach is applied to both, the position-dependent mass Schrödinger equation (PDMSE) and the Schrodinger equation with constant mass (CMSE). This fact enable us to find the factorization operators that relates both Hamiltonians by means of a kinetic energy operator that comes from the proposal of Morrow and Brownstein. With this approach is possible to find the exactly-solvable PDMSE, for any value of the parameters α and γ in the von Roos's Hamiltonian. For that, our proposal can be considered as a unified treatment of the PDMSE because it contains as particular cases, the kinetic energy operators of various authors such as BenDaniel-Duke, Gora-Williams, Zhu-Kroemer and Li-Kuhn among others. To show the usefulness of our result, we show the solvable PDMSE that comes from the harmonic oscillator potential model for the CMSE. The proposal is general and can easily be extended to other potential models and mass distributions which will be given in the extended paper.