Schrodinger Equation with Moving Point Interactions in Three Dimensions

Details Schrodinger Equation with Moving Point Interactions in Three Dimensions Schrodinger Equation with Moving Point Interactions in Three Dimensions

1999-08-06

arxiv.org/abs/math-ph/9908009v1

Physics

Mathematical Physics

AMS Latex file, 15 pages

Scientific paper

We consider the motion of a non relativistic quantum particle in R^3 subject to n point interactions which are moving on given smooth trajectories. Due to the singular character of the time-dependent interaction, the corresponding Schrodinger equation does not have solutions in a strong sense and, moreover, standard perturbation techniques cannot be used. Here we prove that, for smooth initial data, there is a unique weak solution by reducing the problem to the solution of a Volterra integral equation involving only the time variable. It is also shown that the evolution operator uniquely extends to a unitary operator in $L^{2}(R^{3})$.

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