Related papers: Analytic solutions to the problem of Coulomb and c…
We present a mathematically rigorous quantum-mechanical treatment of a two-dimensional nonrelativistic quantum dual theories (with oscillator and Coulomb like potentials) on a plane and compare their spectra and the sets of eigenfunctions.…
Approximate bound state solutions of the spinless Salpeter equation for the Hellmann potential are studied for heavy particles. By using functional analysis method, an analytical expression for the energy levels, and the corresponding…
Exact analytic expression is derived for the matrix elements of the Coulomb interaction in two dimensions in the form of a closed finite sum expression. The orthonormal complete set of eigenfunctions of the harmonic oscillator is used as…
Two possibile applications of the optimized expansion for the free energy of the quantum-mechanical anharmonic oscillator are discussed. The first method is for the finite temperature effective potential; the second one, for the classical…
The generalized pseudospectral method is employed to calculate the bound states of Hulth\'en and Yukawa potentials in quantum mechanics, with special emphases on higher excited states and stronger couplings. Accurate energy eigenvalues,…
For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but…
We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical…
We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using…
A procedure for constructing bound state potentials is given. We show that, under the natural conditions imposed on a radial eigenvalue problem, the only special cases of the general central potential, which are exactly solvable and have…
Non-relativistic potential models are considered of the pure power V(r) = sgn(q) r^q and logarithmic V(r) = ln(r) types. Envelope representations and kinetic potentials are employed to show that these potentials are actually in a single…
An alternative approximation scheme has been used in solving the Schroedinger equation for the exponential-cosine-screened Coulomb potential. The bound state energies for various eigenstates and the corresponding wave functions are obtained…
We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…
Approximate formulas are derived to describe energy loss in a harmonic oscillator that experiences three distinct damping mechanisms: constant-magnitude (Coulomb), velocity-proportional (Stokes), and velocity-squared (Newton), using…
We propose a new quantum computational way of obtaining a ground-state energy and expectation values of observables of interacting Hamiltonians. It is based on the combination of the adiabatic quantum evolution to project a ground state of…
We address quantum systems isospectral to the harmonic oscillator, as those found within the framework of supersymmetric quantum mechanics, as potential resources for continuous variable quantum information. These deformed oscillator…
A numerical method of solving the one-dimensional Schrodinger equation for the regular and irregular continuum states using the phase-amplitude representation is presented. Our solution acquires the correct Dirac-delta normalization by…
An approximation method which combines the perturbation theory with the variational calculation is constructed for quantum mechanical problems. Using the anharmonic oscillator and the He atom as examples, we show that the present method…
Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper…
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…
Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the…