Related papers: Precise variational tunneling rates for anharmonic…
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schr\"odinger…
We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential…
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…
Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developing algorithms to calculate the ground state…
A family of quantum anharmonic oscillators is studied in any finite spatial dimension in the scheme of first quantization and the investigation of their eigenenergies is presented. The statistical properties of the calculated eigenenergies…
An implicit four dimensional regularization is applied to calculate the axial-vector-vector anomalous amplitude. The present technique always complies with results of Dimensional Regularization and can be easily applied to processes…
Applying the time-dependent variational principle of Balian and V\'en\'eroni, we derive variational approximations for multi-time correlation functions in $\Phi^4$ field theory. We assume first that the initial state is given and…
An exactly solvable time-dependent quantum mechanical problem is employed to study the convergence properties of transition amplitudes calculated by using the Schwinger variational principle. A detailed comparison between the amplitudes…
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…
The odderon intercept is calculated directly, from its expression via an average energy of the odderon Hamiltonian, using both trial wave functions in the variational approach and the wave function recently constructed by R.A.Janik and…
We propose an approximate solution of the time-dependent Schr\"odinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the…
The present contribution concerns the computation of energy eigenvalues of a perturbed anharmonic coulombic potential with irregular singularities using a combination of the Sinc collocation method and the double exponential transformation.…
Accurate experimental values for the vibrational ground tone or fundamental vibrational energy splitting of H$_2$, HD, and D$_2$ are presented. Absolute accuracies of $2\times10^{-4}$ cm$^{-1}$ are obtained from Doppler-free laser…
We analyze in this paper a virtual element approximation for the acoustic vibration problem. We consider a variational formulation relying only on the fluid displacement and propose a discretization by means of H(div) virtual elements with…
The energy gap between the first excited state and the ground state is calculated for the quantized anharmonic oscillator in the framework of the functional renormalization group method. The compactly supported smooth regulator is used…
In this work, we present the analytical approach to the evaluation of the conditional measure Wiener path integral. We consider the time-dependent model parameters. We find the differential equation for the variable, determining the…
We analyze the effect of having minimum length on a two dimensional anisotropic simple harmonic oscillator with PT symmetric imaginary interaction perturbatively. First order correction to the general state is calculated analytically to…
To avoid problems with infinite measure, the functional integral for harmonic oscillator can be calculated by time - slicing method with continuum limit procedure proposed Gelfand and Yaglom. In previous article we proved by nonperturbative…
We present an application of a nonstandard approximate method---the finite-rank approximation---to solving the time-independent Schr\"odinger equation for a bound-state problem. The method is illustrated on the example of a…
The nonrelativistic energy of low lying rovibrational levels of HT, DT, and \T\ is determined to an absolute accuracy of $10^{-7}-10^{-8}$ cm$^{-1}$ using the variational method with the four-body nonadiabatic James-Coolidge functions. The…