相关论文: New hydrogen-like potentials
We find matrix factorization corresponding to an anti-diagonal in ${\mathbb C}P^1 \times {\mathbb C}P^1$, and circle fibers in weighted projective lines using the idea of Chan and Leung of Strominger-Yau-Zaslow transformations. For the tear…
Given two spherically symmetric and short range potentials $V_0$ and V_1 for which the radial Schrodinger equation can be solved explicitely at zero energy, we show how to construct a new potential $V$ for which the radial equation can…
Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are…
An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular…
The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods. Furthermore the connection between the model and an anharmonic oscillator had been investigated by methods of KS transformation.
We propose an alternative factorization for the simple harmonic oscillator hamiltonian which includes Mielnik's isospectral factorization as a particular case. This factorization is realized in two non-mutually adjoint operators whose…
We obtained a new class of exactly-solvable potentials by means of the hypergeometric equation for Schrodinger equation, which different from the exactly-solvable potentials introduced by Bose and Natanzon. Using the new class of solvable…
The dynamical symmetries of the Kratzer-type molecular potentials (generalized Kratzer molecular potentials) are studied by using the factorization method. The creation and annihilation (ladder) operators for the radial eigenfunctions…
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the…
The exact bound state spectrum of rationally extended shape invariant real as well as $PT$ symmetric complex potentials are obtained by using potential group approach. The generators of the potential groups are modified by introducing a new…
We use constrained variational minimizing methods to study the existence of periodic solutions with a prescribed energy for a class of second order Hamiltonian systems with a $C^2$ potential function which may have an unbounded potential…
The construction of rationally-extended Morse potentials is analyzed in the framework of first-order supersymmetric quantum mechanics. The known family of extended potentials $V_{A,B,{\rm ext}}(x)$, obtained from a conventional Morse…
We study a new type of symmetry for the hydrogen atom involving algebraic families of groups parametrized by the energy value in the time-independent Schr\"odinger equation. We construct an algebraic family of Harish-Chandra modules from…
Based on the Dirac approach we have developed the relativistic vision of the WKB method for centrally symmetrical potential with mixed Lorenz structure. We have obtained relativistic wavefunctions of light quark and the new rule of…
In 1977, Orlik--Randell construct a nice integral basis of the middle homology group of the Milnor fiber associated to an invertible polynomial of chain type and they conjectured that it is represented by a distinguished basis of vanishing…
A new exact analytically solvable Eckart-type potential is presented, a generalisation of the Hulthen potential. The study through Supersymmetric Quantum Mechanics is presented together with the hierarchy of Hamiltonians and the shape…
We have developed a new simple method to build the exact analytical expression of the eigenenergy as a function of the potential. The idea of our method is mainly based on the partitioning of the potential curve, solving the Schr\"odinger…
We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials…
We want to give a construction as simple as possible of a Borel subset of a product of two Polish spaces. This introduces the notion of potential Wadge class. Among other things, we study the non-potentially closed sets, by proving…
New families of time-dependent potentials related to the parametric oscillator are introduced. This is achieved by introducing some general time-dependent operators that factorize the appropriate constant of motion (quantum invariant) of…