Symmetries and solutions of the three-dimensional Paul trap.
نویسندگان
چکیده
Using the symmetries of the three-dimensional Paul trap, we derive the solutions of the time-dependent Schrodinger equation for this system, in both Cartesian and cylindrical coordinates. Our symmetry calculations provide insights that are not always obvious from the conventional viewpoint.
منابع مشابه
New Solutions for Fokker-Plank Equation of Special Stochastic Process via Lie Point Symmetries
In this paper Lie symmetry analysis is applied in order to find new solutions for Fokker Plank equation of Ornstein-Uhlenbeck process. This analysis classifies the solutions format of the Fokker Plank equation by using the Lie algebra of the symmetries of our considered stochastic process.
متن کاملمحاسبه نواحی سوم, چهارم و پنجم پایداری در دام پاول
The behavior of ions in a Paul trap has been investigated using numerical solution of the set of Mathieus differential equations. Afterwards, the trajectories of two typical ions such as H+ and 208Pb+ in the trap have been obtained using the fourth-order Runge-Kutta method. For specific dimensions of a Paul trap and a given frequency, the stability regions for separation of H+ and 2H+ ions hav...
متن کاملPolynomial and non-polynomial solutions set for wave equation with using Lie point symmetries
This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE). We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry. We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation. A generalized procedure for polynomial solution is pr...
متن کاملA Diffusion Equation with Exponential Nonlinearity Recant Developments
The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...
متن کاملSymmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation
In this paper Lie point symmetries, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation are investigated. First of all Lie symmetries are obtained by using the general method based on invariance condition of a system of differential equations under a prolonged vector field. Then the structure of symmetry ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Optics express
دوره 8 2 شماره
صفحات -
تاریخ انتشار 2001