Related papers: Regularization of the Singular Inverse Square Pote…
Experimental constraints on the gravitational inverse-square law at short range are presented, employing a consistent formalism across a wide range of length scales. We provide comprehensive updates from the past decade, building upon our…
We delineate the scope of research on the completeness of eigenstates in quantum mechanics. Based on the limit of the potential function at infinity, the proof of completeness is divided into eight cases, and theoretical proofs or numerical…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the…
In this paper, we study supersymmetry in quantum mechanics using the generalized uncertainty principle (GUP), or in other words, generalized supersymmetry in quantum mechanics. We construct supersymmetry in the generalized form of the…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
We study quantum mechanics on a curved wire by approximating the physics around the curved region by three parameters coming from the boundary conditions given by the two interval Sturm-Liouville theory. Since the geometric potential on a…
We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…
Many theories that attempt to formulate a quantum description of gravity suggest the existence of a fundamental minimum length scale. A popular method for incorporating this minimum length is through a modification of the Heisenberg…
We find the coordinate space wave functions, maximal localization states, and quasiposition wave functions in a GUP framework that implies a minimal length uncertainty using a formally self-adjoint representation. We show that how the…
Self-similar potentials generalize the concept of shape-invariance which was originally introduced to explore exactly-solvable potentials in quantum mechanics. In this article it is shown that previously introduced algebraic approach to the…
We establish a relation between the solution of a relativistic bound state equation in quantum mechanics and the field representation of a bound state with the aid of creation and annihilation operators. We show that a bound system can be…
We discuss the regularization of attractive singular potentials $-\alpha _{s}/r^{s}$, $s\geq 2$ by infinitesimal imaginary addition to interaction constant $\alpha_{s}=\alpha_{s}\pm i0$. Such a procedure enables unique definition of…
We examine several zero-range potentials in non-relativistic quantum mechanics. The study of such potentials requires regularization and renormalization. We contrast physical results obtained using dimensional regularization and cutoff…
A simple formalism for exploring quantum scattering and possible bound states in an arbitrary symmetric and localized potential in a unified way is presented. The symmetric square barrier and well potentials are used for illustrating the…
Using phase-equivalent supersymmetric partner potentials, a general result from the inverse problem in quantum scattering theory is illustrated, i.e., that bound-state properties cannot be extracted from the phase shifts of a single partial…
We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak…
The possibility of the existence of small correction terms to the canonical commutation relations and the uncertainty relations has recently found renewed interest. In particular, such correction terms could induce finite lower bounds…
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable…