Development and refinement of the Variational Method based on Polynomial Solutions of Schrödinger Equation

The variational method is known as a powerful and preferred technique to find both analytical and numerical solutions for numerous forms of anharmonic oscillator potentials. In the present study, we considered certain conditions for the choice of the trial wave function. The current form of the trial wave function is based on the possible polynomial solutions of the Schrödinger equation. The advantage of our modified variational method is its ability to reduce the calculation steps and hence computation time. Also, we compared the results provided by our modified method with the results obtained by different methods in general but particularly Numerov method for the same problem.

Вариационная модель низкоразмерного магнетика

A variational method with nonlocal trial function is developed for quantum one-dimensional systems. It is applied to the XXZ spin-1/2 chain with an alternating magnetic field. A four-node trial wave function for the fermionic representation of the model is constructed. The results obtained in the model with an extended trial wave function demonstrate a significant increase in the accuracy of the ground state energy in the region of critical behavior compared with the solutions obtained previously. A method for calculation of the spin correlation function are discussed.

Variational Solution of Steady-Structure in Exciton-Polariton Condensates with a Modified Lagrangian Approach

Exciton-polariton condensate is a new kind of system exhibiting spontaneous coherence, which is a new quantum dissipation system. Numerical simulation and analytical methods can be used to study the static and dynamical properties of exciton-polariton condensate. In this paper, A modified Lagrangian method is developed for exciton-polariton system to find the steady-state structure and regimes among the parameters of the system, and two new forms of trial wave function are proposed. The modified Lagrangian method is successfully applied to the exciton-polariton system described by the open-dissipative Gross-Pitaevskii equation for the first time. Furthermore, static version of the modified Lagrangian method provides stationary shape of the steady-state structure, while the time-dependent version can be used to study small amplitude oscillations around stationary states. On the one hand, comparison of the profiles for steady-state structure, predicted by the modified Lagrangian and those found from numerical solution of the open-dissipative Gross-Pitaevskii(dGP) equation shows good agreement, thereby proving the accuracy of the trial wave function and validating the proposed approach. Particularly, this new method promotes the deeper cognition and understanding for the dissipative exciton-polariton system and is helpful to explore the mechanism of the gain and dissipation effect on the steady-state structure of the system.

THE DIFFUSION QUANTUM MONTE CARLO METHOD: DESIGNING TRIAL WAVE FUNCTIONS FOR NiO

A brief overview of the diffusion quantum Monte Carlo method is given. The importance of the trial wave function is emphasised and we discuss how to design satisfactory forms for transition metal monoxides. Some results of a diffusion quantum Monte Carlo study of NiO are reported.