Related papers: Effective Mass Quantum Systems with Displacement O…
We write Schr\"odinger equation for the Coulomb potential in both de Sitter and Anti-de Sitter spaces using the Extended Uncertainty Principle formulation. We use the Nikiforov-Uvarov method to solve the equations. The energy eigenvalues…
A global solution of the Schr\"odinger equation, obtained recently within the wave operator formalism for explicitly time-dependent Hamiltonians [J. Phys. A: Math. Theor. 48, 225205 (2015)], is generalized to take into account the case of…
Active matter is driven out of equilibrium by a local influx of energy. While classical active matter has been extensively studied, the extension of active matter concepts to quantum systems has been explored far less. In this work we…
In this paper, we introduce an inverse problem of a Schr\"odinger type variable nonlocal elliptic operator $(-\nabla\cdot(A(x)\nabla))^{s}+q)$, for $0<s<1$. We determine the unknown bounded potential $q$ from the exterior partial…
We formulate an inverse problem for an uncoupled space-time fractional Schr\"odinger equation on closed manifolds. Our main goal is to determine the fractional powers and the Riemannian metric (up to an isometry) simultaneously from the…
It is shown the role of a scalar potential in the Schr\"{o}dinger equation for a steady-state two-particle system is equivalent to an isometric entanglement of the position coordinates of the particles in space and time. The entangled…
We consider the Schr\"odinger equation for hydrogen-like atom with Coulomb potential and non-point ball nucleus. The eigenvalues and eigenfunctions of the operator given by an arbitrary rotation-invariant boundary value problem on the…
We give a simple demonstration that the Schr\"odinger equation may be recast as a self-contained second-order Newtonian law for a congruence of spacetime trajectories. This provides a pictorial representation of the quantum state as the…
We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum…
We consider the inverse coefficient problem of simultaneously determining the space dependent electromagnetic potential, the zero-th order coupling term and the first order coupling vector of a two-state Schr\"odinger equation in a bounded…
Assuming Coulomb-like as well as confining scalar potential, we have solved Shr\"odinger equation perturbatively in $1/m_Q$ with a heavy quark mass $m_Q$. The lowest order equation is examined carefully. Mass levels are fitted with…
Few-body problems involving Coulomb or gravitational interactions between pairs of particles, whether in classical or quantum physics, are generally handled through a standard multipole expansion of the two-body potentials. We discuss an…
The kinetic energy operator with position-dependent-mass in plane polar coordinates is obtained. The separability of the corresponding Schr\"odinger equation is discussed. A hypothetical toy model is reported and two exactly solvable…
In this paper, we consider the Cauchy problem for the nonlinear Schr\"odinger equations with repulsive inverse-power potentials \[ i \partial_t u + \Delta u - c |x|^{-\sigma} u = \pm |u|^\alpha u, \quad c>0. \] We study the local and global…
We show in this paper that the basic representations of position and momentum in a quantum mechanical system, that are guided by a generalized uncertainty principle and lead to a corresponding one-parameter eigenvalue problem, can be…
In this work, we investigate the electronic transport properties of curved two-dimensional quantum systems with a position-dependent mass (PDM). We found the Schr\"odinger equation for a general surface following the da Costa approach,…
The three-dimensional Schr\"odinger equation with a position-dependent (effective) mass is studied in the framework of Supersymmetrical (SUSY) Quantum Mechanics. The general solution of SUSY intertwining relations with first order…
Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the…
Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least one second order…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…