Related papers: Polymer quantization, singularity resolution and t…
We apply a singularity resolution technique utilized in loop quantum gravity to the polymer representation of quantum mechanics on R with the singular -1/|x| potential. On an equispaced lattice, the resulting eigenvalue problem is identical…
Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate…
A general quantization rule for bound states of the Schrodinger equation is presented. Like fundamental theory of integral, our idea is mainly based on dividing the potential into many pieces, solving the Schr\"odinger equation, and…
We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
In this thesis, we study a quantization condition in relation to the solvability of Schr\"{o}dinger equations. This quantization condition is called the SWKB (supersymmetric Wentzel-Kramers-Brillouin) quantization condition and has been…
We cast the quantum chemistry problem of computing bound states as that of solving a set of auxiliary eigenvalue problems for a family of parameterized compact integral operators. The compactness of operators assures that their spectrum is…
An exact quantization rule for the bound states of the one-dimensional Schr\"{o}dinger equation is presented and is generalized to the three-dimensional Schr\"{o}dinger equation with a spherically symmetric potential.
Polymer quantization was discovered during the construction of Loop Quantum Cosmology. For the simplest quantum theory of one degree of freedom, the implications for dynamics were studied for the harmonic oscillator as well as some other…
The one-dimensional Schr\"{o}dinger equation for a class of potentials $V(|x|)$ which vanish at infinity and present dominant singularity at the origin in the form $\alpha /|x|^{\beta}$ ($0<\beta \leq 2$) is investigated. The Hermiticity of…
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…
We study the radial Schr\"odinger equation for a particle of mass $m$ in the field of a singular attractive $g^2/{r^4}$ potential with particular emphasis on the bound states problem. Using the regularization method of Beane \textit{et…
We study the bound states of a quantum mechanical system consisting of a simple harmonic oscillator with an inverse square interaction, whose interaction strength is governed by a constant $\alpha$. The singular form of this potential has…
We consider a non relativistic charged particle in a 1-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) time depending electric field. It is represented by a complex…
The stationary 1D Schr\"odinger equation with a polynomial potential $V(q)$ of degree N is reduced to a system of exact quantization conditions of Bohr-Sommerfeld form. They arise from bilinear (Wronskian) functional relations pairing…
We study the polymeric nature of quantum matter fields using the example of a Friedmann-Lemaitre-Robertson-Walker universe sourced by a minimally coupled massless scalar field. The model is treated in the symmetry reduced regime via…
We study the quantum mechanics of self-gravitating thin shell collapse by solving the polymerized Wheeler-DeWitt equation. We obtain the energy spectrum and solve the time dependent equation using numerics. In contradistinction to the…
The quantum mechanical bound states of the $-{\alpha}/x^2$ potential are truly anomalous. We revisit this problem by adopting a slightly modified version of this potential, one that adopts a cutoff in the potential arbitrarily close to the…
Bound-state solutions of the singular harmonic oscillator and singular Coulomb potentials in arbitrary dimensions are generated in a simple way from the solutions of the one-dimensional generalized Morse potential. The nonsingular harmonic…
We quantize the 1-dimensional 3-body problem with harmonic and inverse square pair potential by separating the Schr\"odinger equation following the classic work of Calogero, but allowing all possible self-adjoint boundary conditions for the…