TAILIEUCHUNG - Quantum diffusion monte carlo method for low-dimentional systems

We will show that Schrodinger equations for low-dimensional systems can be solved by the method of quantum Diffusion Monte Carlo (DMC). The wave function and energy in a ground state are found for the two-dimensional harmonic oscillator, quantum wells, quantum wires and quantum dots. This is great approach for problems of low-dimensional systems. In this paper, the sign of the wave function is not treated. | JOURNAL OF SCIENCE OF HNUE DOI Mathematical and Physical Sci. 2015 Vol. 60 No. 7 pp. 81-87 This paper is available online at http QUANTUM DIFFUSION MONTE CARLO METHOD FOR LOW-DIMENTIONAL SYSTEMS Nguyen The Lam Faculty of Physics Hanoi Pedagogical University No. 2 Abstract. We will show that Schr odinger equations for low-dimensional systems can be solved by the method of quantum Diffusion Monte Carlo DMC . The wave function and energy in a ground state are found for the two-dimensional harmonic oscillator quantum wells quantum wires and quantum dots. This is great approach for problems of low-dimensional systems. In this paper the sign of the wave function is not treated. Keywords Schr odinger equations method of quantum Diffusion Monte Carlo low-dimensional systems. 1. Introduction Nowadays low-dimensional materials are produced with high technologies. Examples of these are thin film InAs AlSb super lattice 1 InGaAs GaAs quantum well 2 CdTe GaAs and GaP quantum wire 3 4 PbS quantum dot 5 and nano materials. In general these materials are called low-dimensional systems and in theory these systems are governed by Schr odinger equations. The solving of the Schr odinger equations for these systems must be done for theoretical problems. In fact these equations can be solved analytically in some simple cases for complex energy potentials they can not be solved. In this paper the Quantum diffusion Monte Carlo DMC method will be applied for low-dimensional systems. With this method the wave function and energy in the ground state may be found. The solution of a time-dependent Schr odinger equation may be written as a linear superposition of stationary states in which the time-dependence is given by phase factor exp iEn t where En is the energy in the n-th level of the quantum system. An energy scale may be chosen such that all energies are positive. In the DMC method the time-dependent Schr odinger equation is considered as .

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