# Two electron quantum dot in magnetic ﬁeld

Susmita Roy, Institut für Theoretische Physik, Universität Regensburg (Germany)

**Abstract**

Solution of interacting classical many body system is diﬃcult to achieve, since the integration of the equations of motions couples all positions and momentum of the particles contained in the system. Quantum mechanics adds some approximations to solve this type of problems. We analyze the time dependent dynamics of interacting two electron problem in absence of any conﬁning potential, on the basis of Time Dependent Variational Principle (TDVP), which relate the classical and quantum mechanical equations of motion. The motion is conﬁned to a two dimensional plane, which is commonly the case in nano devices. Any variational principle can produce a result but its accuracy and quality depends upon the choise of variational wave functions which are choosen with physical insight into the problem at hand. We are using the coherent states for variational wave function in two diﬀerent ways. On the one hand, we are treating the full dynamics instead of the dynamics of relative motion. On the other hand, we will not allow a variation of the width of coherent state and use the properties of Bargmann representation for the coherent states.