Two-dimensional time-dependent point interactions

  • Raffaele Carlone

    Università degli Studi di Napoli Federico II, Italy
  • Michele Correggi

    Università degli Studi Roma Tre, Italy
  • Rodolfo Figari

    Università degli Studi di Napoli Federico II, Italy
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We study the time-evolution of a quantum particle subjected to time-dependent zero-range forces in two dimensions. After establishing a conceivable ansatz for the solution to the Schrödinger equation, we prove that the wave packet time-evolution is completely specified by the solutions of a system of Volterra-type equations – the charge equations – involving the coefficients of the singular part of the wave function, thus extending to the two-dimensional case known results in one and three dimensions.