Renormalized Contact Potential in Two Dimensions
R. J. Henderson, S. G. Rajeev
Abstract
We obtain for the attractive Dirac delta-function potential in two-dimensional quantum mechanics a renormalized formulation that avoids reference to a cutoff and running coupling constant. Dimensional transmutation is carried out before attempting to solve the system, and leads to an interesting eigenvalue problem in N-2 degrees of freedom (in the center of momentum frame) when there are N particles. The effective Hamiltonian for N-2 particles has a nonlocal attractive interaction, and the Schrodinger equation becomes an eigenvalue problem for the logarithm of this Hamiltonian. The 3-body case is examined in detail, and in this case a variational estimate of the ground-state energy is given.
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