Control of a Quantum Particle in a Moving Potential Well
نویسنده
چکیده
The control is the potential well absolute position. For two kinds of potential shape (periodic and box), we propose approximated solutions to the stead-state motion planing problem: steering in finite time the particle from an initial well position to a final well position, the initial and final particle energies being identical. This problem is a quantum analogue of the water tank problem, where a tank filled with liquid is moved from one position where the surface is horizontal to another position where the surface is also horizontal.
منابع مشابه
Berry phase for a particle in an infinite spherical potential well with moving wall
In this paper we calculate the Berry phase for a wave function of a particle in an infinite spherical potential well with adiabatically varying. In order to do this, we need the solutions of the corresponding Schrödinger equation with a time dependent Hamiltonian. Here, we obtain these solutions for the first time. In addition, we calculate the Berry phase in one dimensional case for an infinit...
متن کاملذره در چاه کوانتومی با دیواره متحرک
We study the problem of a quantum particle in an infinite one dimensional potential well with a moving wall. Based on the effective Hamiltonian approach and using the gauge transformation concepts, we show that the effect of the moving wall appears as an extra phase factor in the wave function which depends on the velocity of the wall.
متن کاملWhen the classical & quantum mechanical considerations hint to a single point; a microscopic particle in a one dimensional box with two infinite walls and a linear potential inside it
In this paper we have solved analytically the Schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. Based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...
متن کاملVibration Analysis of Magneto-Electro-Elastic Timoshenko Micro Beam Using Surface Stress Effect and Modified Strain Gradient Theory under Moving Nano-Particle
In this article, the free vibration analysis of magneto-electro-elastic (MEE) Timoshenko micro beam model based on surface stress effect and modified strain gradient theory (MSGT) under moving nano-particle is presented. The governing equations of motion using Hamilton’s principle are derived and these equations are solved using differential quadrature method (DQM). The effects of dimensionless...
متن کاملQUANTUM TUNNELING IN MEDIUMS WITH LINEAR AND NONLINEAR DISSIPATION
We have applied the method of integration of the Heisenberg equation of motion proposed by Bender and Dunne, and M. Kamella and M. Razavy to the potential V(q) = v q - µ q with linear and nonlinear dissipation. We concentrate our calculations on the evolution of basis set of Weyl Ordered Operators and calculate the mean position , velocity , the commutation relation [q, p], and the energ...
متن کامل