Related papers: General approach to potentials with two known leve…
We investigate two methods of obtaining exactly solvable potentials with analytic forms.
In this work we study the quantum system with the symmetric Razavy potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun functions. The eigenvalues have to be calculated numerically.…
We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a…
Using an accurate semi-analytic wavefunction for two electron atoms, we construct the external potential for varying strength of electron-electron (e-e) interaction. Using this potential we explicitly calculate the energy of their positive…
A summary is presented of the properties of the coefficient matrices formed by expanding the two-body reduced density matrix in a complete set of two-electron wave functions. Calculating the relationship between the many electron wave…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
Probabilistic models can be defined by an energy function, where the probability of each state is proportional to the exponential of the state's negative energy. This paper considers a generalization of energy-based models in which the…
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
We propose a new SUSY method for construction of the quasi-exactly solvable (QES) potentials with three known eigenstates. New QES potentials and corresponding energy levels and wave functions of the ground state and two lowest excited…
We propose a naive unification of Electromagnetism and General Relativity based on enlarging the gauge group of Ashtekar's new variables. We construct the connection and loop representations and analyze the space of states. In the loop…
A novel analytically solvable deformed Woods-Saxon potential is investigated by means of the Supersymmetric Quantum Mechanics. Hamiltonian hierarchy method and the shape invariance property are used in the calculations. The energy levels…
Pseudopotential theory has greatly driven first-principles calculations in materials, replacing the explicit treatment of the chemically inert core electrons with an effective potential acting only on the valence states. This is inherently…
In this work we prove that the possibility of superactivation of quantum channel capacities is determined by the mathematical properties of the quantum relative entropy function. Before our work this fundamental and purely mathematical…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…
The adaptation rule for Vector Quantization algorithms, and consequently the convergence of the generated sequence, depends on the existence and properties of a function called the energy function, defined on a topological manifold. Our aim…
Matrix elements of potential energy are examined in detail. We consider a model problem - a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and…
The grand potential of a system of interacting electrons is considered as a stationary point of a self-energy functional. It is shown that a rigorous evaluation of the functional is possible for self-energies that are representable within a…
Motivated by the interest in non-relativistic quantum mechanics for determining exact solutions to the Schrodinger equation we give two potentials that are conditionally exactly solvable. The two potentials are partner potentials and we…
In this work we discuss about the problem of an electrically charged particle placed on the symmetry axis of an electrically charged ring in a quantum viewpoint. This problem should be an expanded version of the usual quantum ring and…
The quantum mechanical behavior of a particle in a double well defies our intuition based on classical reasoning. Not surprisingly, an asymmetry in the double well will restore results more consistent with the classical picture. What is…