Related papers: Effective-mass Schroedinger equation and generatio…
We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation. Specifically, we show that if the sampling function is a non-constant H\"older…
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…
Within the Schroedinger Electric Representation we analytically calculate the complete wave functional obeying Gauss' law with static SU(2) sources in (1+1)-dimensions. The effective potential is found to be linear in the distance between…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
Orthogonal Polynomials in Quantum Mechanics. Exact solutions of the Schrodinger equation with the hyperbolic Scarf potential (Scarf II) in terms of Romanovski polynomials. Among the applications included is the solution of the problem of an…
A charged particle in the presence of a magnetic field is studied in the position dependent operator formalism. Instead of a quantum harmonic oscillator, the solution of the resulting Schr\"odinger-like equation is the one for the Morse…
We study the representation theory of the solution space of the one-dimensional Schr\"{o}dinger equation with time-dependent potentials that posses $\mathfrak{sl}_2$-symmetry. We give explicit local intertwining maps to multiplier…
In the Kirchhoff model of a biopolymer, conformation dynamics can be described in terms of solitary waves, for certain special cross-section asymmetries. Applying this to the problem of electron transport, we show that the quantum effective…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
In this study, we consider two nonlinear Schr\"{o}dinger-type models that are derived by R L. Frank, F. M\'{e}hats, C. Sparber [arXiv:1611.01574] to study 3D nonlinear Schr\"{o}dinger equations under strong magnetic fields. One model is…
The exactly solvable Schr\"{o}dinger equations with the conventional shape-invariant potentials are known to be related with each other through point cannonical transformations. In this paper, we extend the idea to integral formulae called…
The second order $N$-dimensional Schr\"odinger equation with pseudoharmonic potential is reduced to a first order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution…
In the present work, we studied the q-deformed Morse and harmonic oscillator systems with appropriate canonical commutation algebra. The analytic solutions for eigenfunctions and energy eigenvalues are worked out using time-independent…
In this short paper, we investigate the consequences of observer dependence of the quantum effective potential for an interacting field theory. Specializing to $d+2$ dimensional Euclidean Rindler space, we develop the formalism to calculate…
A complete and consistent inversion technique is proposed to derive an accurate interaction potential from an effective-range function for a given partial wave in the neutral case. First, the effective-range function is Taylor or Pad\'e…
In this article we revisit the observability of the Schr\"odinger equation on the two-dimensional torus. In contrast to the Schr\"odinger operator with a purely electric potential, for which any non-empty open set guarantees observability,…
The Schr\" odinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring…
This paper is motivated by a gauged Schr\"odinger equation in dimension 2 including the so-called Chern-Simons term. The study of radial stationary states leads to the nonlocal problem: $$ - \Delta u(x) + \left(\omega +…
We consider the stochastic nonlinear Schr\"odinger equations (SNLS) posed on $d$-dimensional tori with either additive or multiplicative stochastic forcing. In particular, for the one-dimensional cubic SNLS, we prove global well-posedness…
The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is…