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A systematic procedure to study one-dimensional Schr\"odinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting…
Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and…
A new SU(1, 1) position-dependent effective mass coherent states (PDEM CS) related to the shifted harmonic oscillator (SHO) are deduced. This is accomplished by applying a similarity transformation to the generally deformed oscillator…
The Schroedinger equation for position-dependent mass singular oscillators is solved by means of the factorization method and point transformations. These systems share their spectrum with the conventional singular oscillator. Ladder…
Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…
A covariant non-local extention if the stationary Schr\"odinger equation is presented and it's solution in terms of Heisenbergs's matrix quantum mechanics is proposed. For the special case of the Riesz fractional derivative, the calculation…
By using a point canonical transformation starting from the constant-mass Schr\"odinger equation for the Morse potential, it is shown that a semi-infinite quantum well model with a non-rectangular profile associated with a…
In this paper, we study the time-independent Schr\"odinger equation within the formalism of position dependent effective mass. For a generalized decomposition of the non-central effective potential, the deformed Schr\"odinger equation can…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
In this survey the contemporary results concerning supersymmetries in generalized Schr\"odinger equations are presented. Namely, position dependent mass Sch\"odinger equations are discussed as well as the equations with matrix potentials.…
It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle…
Revisiting the issue associated with Position-Dependent Mass (PDM), we reaffirm that the appropriate framework for addressing a generic PDM is the symmetrization proposed by BenDaniel and Duke. To accomplish this result adopts the effective…
We consider the energy critical nonlinear Schr\"{o}dinger equation in dimensions $d \ge 3$ with a harmonic oscillator potential $V(x) = \tfrac{1}{2} |x|^2$. When the nonlinearity is defocusing, we prove global wellposedness for all initial…
A new method for generating exactly solvable Schr\"odinger equations with a position-dependent mass is proposed. It is based on a relation with some deformed Schr\"odinger equations, which can be dealt with by using a supersymmetric quantum…
The exact solvability and impressive pedagogical implementation of the harmonic oscillator creation and annihilation operators make it a problem of great physical relevance and the most fundamental one in quantum mechanics. So would be the…
In this paper, we present an analysis of the equation $\ddot{x} - (1/2x) \dot{x}^2 + 2 \omega^2 x - 1/8x = 0$, where $\omega > 0$ and $x = x(t)$ is a real-valued variable. We first discuss the appearance of this equation from a…
The general equation from previous work is specialized to a quadratic potential $V(r)=-a+\frac12 f r^2$ acting in the space of spherically symmetric S wave functions. The fine and hyperfine interaction creates then a position dependent mass…
A one-dimensional Schr\"odinger equation with position-dependent effective mass in the kinetic energy operator is studied in the framework of an $so(2,1)$ algebra. New mass-deformed versions of Scarf II, Morse and generalized…
We use the Fourier operator to transform a time dependent mass quantum harmonic oscillator into a frequency dependent one. Then we use Lewis-Ermakov invariants to solve the Schr\"odinger equation by using squeeze operators. Finally we give…
We explore the quantization of classical models with position-dependent mass (PDM) terms constrained to a bounded interval in the canonical position. This is achieved through the Weyl-Heisenberg covariant integral quantization by properly…