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A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
A one-dimensional quantum harmonic oscillator perturbed by a smooth compactly supported potential is considered. For the corresponding eigenvalues $\lambda_n$, a complete asymptotic expansion for large $n$ is obtained, and the coefficients…
The use of the hyperspherical harmonic (HH) basis in the description of bound states in an $A$-body system composed by identical particles is normally preceded by a symmetrization procedure in which the statistic of the system is taken into…
We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with…
An explicit demonstration is given of a harmonic oscillator in equilibrium approaching the equilibrium of a corresponding interacting system by coupling it to a thermal bath consisting of a continuum of harmonic oscillators.
We write a computer program that uses the recursion relation to calculate wave function in the harmonic-oscillator potential for specified values of E/hv (with its deviation 0.001) containing only even numbers of v (0,2,4,...). In this…
We derive the energy levels associated with the even-parity wave functions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical…
The large-N expansion technique is tested via an anomalous, soft-core potential which admits the tunneling through its central barrier. The precision of the approximation is found sensitive to the asymptotic component of the interaction.…
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…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be…
The quantum harmonic oscillator is the fundamental building block to compute thermal properties of virtually any dielectric crystal at low temperatures in terms of phonons, extended further to cases with anharmonic couplings, or even…
We study the supersymmetric partners of the harmonic oscillator with an infinite potential barrier at the origin and obtain the conditions under which it is possible to add levels to the energy spectrum of these systems. It is found that…
The three-body continuum Coulomb problem is treated in terms of the generalized parabolic coordinates. Approximate solutions are expressed in the form of a Lippmann-Schwinger type equation, where the Green's function includes the leading…
Coulomb wave functions are difficult to compute numerically for extremely low energies, even with direct numerical integration. Hence, it is more convenient to use asymptotic formulas in this region. It is the object of this paper to derive…
Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only…
The oscillator parameter in nuclei is refitted to reproduce the available charge radius data. As an important improvement, we include the Coulomb term evaluated within the assumption of a uniformly charged sphere, and take into account the…
Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of…
A convenient way to calculate $N$-particle quantum partition functions is by confining the particles in a weak harmonic potential instead of using a finite box or periodic boundary conditions. There is, however, a slightly different…
The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale. By using a perturbative approach, we analytically…