Related papers: Quantum equivalent of the Bertrand's theorem
We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…
For zero energy, $E=0$, we derive exact, classical and quantum solutions for {\em all} power-law oscillators with potentials $V(r)=-\gamma/r^\nu$, $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions…
In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis $|1\rangle$. It is found that, for such a kind of…
An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar approximation theory. In order to derive…
Using a formulation of quantum mechanics based on orthogonal polynomials in the energy and physical parameters, we present a method that gives the class of potential functions for exactly solvable problems corresponding to a given energy…
The existence of a positive solution to a class of Choquard equations with potential going at a positive limit at infinity possibly from above or oscillating is proved. Our results include the physical case and do not require any symmetry…
This letter examines the consequences of a recently proposed modification of the postulate of equal {\it a priori} probability in quantum statistical mechanics. This modification, called the {\it quantum microcanonical postulate} (QMP),…
Schroedinger bound-state problem in D dimensions is considered for a set of central polynomial potentials (containing 2q coupling constants). Its polynomial (harmonic-oscillator-like, quasi-exact, terminating) bound-state solutions of…
The purpose of this Comment is to show that the solutions to the zero energy Schr\"odinger equations for monomial central potentials discussed in a recently published Letter, may also be obtained from the corresponding free particle…
We constrain the possible bound-state solutions of the spinless Salpeter equation (the most obvious semirelativistic generalization of the nonrelativistic Schr\"odinger equation) with an interaction between the bound-state constituents…
We analyze the calculation of bound states for a nonrelativistic spin-half neutral particle under the influence of a Coulomb-like potential induced by Lorentz symmetry breaking effects. We show that the truncation condition proposed by the…
It is well known in classical mechanics that, the frequencies of a periodic system can be obtained rather easily through the action variable, without completely solving the equation of motion. The equivalent quantum action variable…
We examine various generalizations, e.g. exactly solvable, quasi-exactly solvable and non-Hermitian variants, of a quantum nonlinear oscillator. For all these cases, the same mass function has been used and it has also been shown that the…
Quantum mechanics in a noncommutative plane is considered. For a general two dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter ($\theta$) and explicit…
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The…
In the present article, we describe a method of introducing the harmonic potential into the Klein-Gordon equation, leading to genuine bound states. The eigenfunctions and eigenenergies are worked out explicitly.
The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to…
In this Letter the bound states of (2+1) Dirac equation with the cylindrically symmetric $\delta (r-r_{0})$-potential are discussed. It is surprisingly found that the relation between the radial functions at two sides of $r_{0}$ can be…
The method of potential envelopes is used to analyse the bound-state spectrum of the Schroedinger Hamiltonian H = -Delta -v/(r+b), where v and b are positive. We established simple formulas yielding upper and lower energy bounds for all the…
We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic quantum dual theories (with oscillator and Coulomb-like potentials) and compare their spectra and the sets of eigenfunctions. We…