arXiv subjects
Publications and source records attributed to M. Izadparast.
We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schrödinger equation. The extended probability and particle current densities are found which satisfy the continuity equation.
We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schrodinger equation. The extended probability and particle current densities are found which satisfy the continuity equation.
In the present study, the concept of a quantum particle with step momentum is introduced. The energy eigenvalues and eigenfunctions of such particles are obtained in the context of the generalized momentum operator, proposed recently in [13, 14]. While, the number of bound states with real energy for the particles with Hermitian step momentum inside a square well is infinite, it is finite for a particle with \mathcal{PT} -symmetric momentum.
We develop further the concept of generalized extended momentum operator (GEMO), which has been introduced very recently in \citep{M.H2}, and propose the so called $\mathcal{PT}$-symmetric GEMO. In analogy with GEMO, the $\mathcal{PT}$-symmetric GEMO also satisfies the extended uncertainty principle (EUP) relation. Moreover, the corresponding Hamiltonian that is constructed upon the $\mathcal{PT}$-symmetric GEMO, with a real or $\mathcal{PT}$-symmetric potential, remains non-Hermitian but $\mathcal{PT}$-symmetric and consequently its energy and momentum eigenvalues are real. We apply our formalism to a quasi-free quantum particle and the exact solutions for the energy spectrum are presented.
We study and generalize the momentum operator satisfying the extended uncertainty principle relation (EUP). This generalized extended momentum operator (GEMO) consists of an arbitrary auxiliary function of position operator, $μ\left( x\right) $, in such a combination that not only GEMO satisfies the EUP relation but also it is Hermitian. Next, we apply the GEMO to construct the generalized one-dimensional Schrödinger equation. Upon using the so called point canonical transformation (PCT), we transform the generalized Schrödinger equation from $x$-space to $z$-space where in terms of the transformed coordinate, $z$, it is of the standard form of the Schrödinger equation. In continuation, we study two illustrative examples and solve the corresponding equations analytically to find the energy spectrum.