Related papers: Wronskian method for bound states
Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
A normalizable static supersymmetric bound ground state annihilated by the super-generators has got zero number of internal nodes in the framework of one-dimensional supersymmetric quantum mechanics. The super-generator transformations…
We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
Using the Wick-Cutkosky model and an extended version (massive exchange) of it, we have calculated the bound states in a quantum field theoretical approach. In the light-front formalism we have calculated the bound-state mass spectrum and…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
Scattering states with LEED asymptotics are calculated for a general non-muffin tin potential, as e.g. for a pseudopotential with a suitable barrier and image potential part. The latter applies especially to the case of low lying conduction…
We propose a method to calculate wave functions and energies not only of the ground state but also of low-lying excited states using a deep neural network and the unsupervised machine learning technique. For systems composed of identical…
We investigate the work dissipated during the irreversible unfolding of single molecules by mechanical force, using the simplest model necessary to represent experimental data. The model consists of two levels (folded and unfolded states)…
The determination of the eigenenergies of a quantum anharmonic oscillator consists merely in finding the zeros of a function of the energy, namely the Wronskian of two solutions of the Schroedinger equation which are regular respectively at…
At the lower edge of the energy continuum the birth of an isolated quantum bound state is studied as caused by an infinitesimally small change of the interaction. In our model a single, asymptotically free massive quantum particle is…
The radial part of the Klein-Gordon equation for the Woods-Saxon potential is solved. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for any $l$ states. The…
One to one correspondence between the decay law of the von Neumann-Wigner type potentials and the asymptotic behaviour of the wave functions representing bound states in the continuum is established.
A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…
The confluent second-order supersymmetric quantum mechanics, for which the factorization energies tend to a single value, is studied. We show that the Wronskian formula remains valid if generalized eigenfunctions are taken as seed…
Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…
The variable-phase approach is applied to scattering and bound states in an attractive Coulomb potential, statically screened by a two-dimensional (2D) electron gas. A 2D formulation of Levinson's theorem is used for bound-state counting…
The energy spectra and the wave function depending on the c-factor are investigated for a more general Woods-Saxon potential (MGWSP) with an arbitrary l - state. The wave functions are expressed in terms of the Jacobi polynomials. Two…
Quasi-exactly solvable rational potentials with known zero-energy solutions of the Schro\" odinger equation are constructed by starting from exactly solvable potentials for which the Schr\" odinger equation admits an so(2,1) potential…