Renormalization in Nonrelativistic Quantum Mechanics

Abstract

The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin exhibits ultraviolet divergence. The use of renormalization techniques in these problems leads to finite converged results for both the exact and perturbative solutions. The renormalization procedure is carried out for the quantum two-body problem in different partial waves for a minimal potential possessing only the threshold behavior and no form factors. The renormalized perturbative and exact solutions for this problem are found to be consistent with each other. The useful role of the renormalization group equations for this problem is also pointed out.

16 pages

References in corpus (2)

• Lattice Discretization in Quantum Scattering
• Application of Renormalization to Potential Scattering

Cited by in corpus (28)

• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• Nuclear effective field theory: status and perspectives
• A renormalisation-group treatment of two-body scattering
• Renormalization of the Inverse Square Potential
• A hint of renormalization
• Low Energy Theorems For Nucleon-Nucleon Scattering
• The Renormalization Group Limit Cycle for the 1/r^2 Potential
• The Polarizability of the Deuteron
• Testing Low Energy Theorems in Nucleon-Nucleon Scattering
• About the Equivalence of Cut-off and Renormalised Effective Field Theories
• Cooper pair dispersion relation for weak to strong coupling
• Renormalization in conformal quantum mechanics
• The Anapole Form Factor of the Deuteron
• Universal scaling in a trapped Fermi super-fluid in the BCS-unitarity crossover
• Scheming in Dimensional Regularization
• Systematic Power Counting in Cutoff Effective Field Theories for Nucleon-Nucleon Interactions and the Equivalence With PDS
• Linear to quadratic crossover of Cooper pair dispersion relation
• On the renormalization of contact interactions for the configuration-interaction method in two dimensions
• Universal behavior of a trapped Fermi superfluid in the BCS-unitarity crossover
• Universal scaling in BCS superconductivity in two dimensions in non-s waves
• Tensor Polarized Gamma-Deuteron Compton Scattering in Effective Field Theory
• Dimensional regularization applied to nuclear matter with a zero--range interaction
• Interaction of Relativistic Bosons with Localized Sources on Riemannian Surfaces
• Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity
• Renormalization of chiral nuclear forces with multiple subtractions in peripheral channels
• Dimensional versus cut-off renormalization and the nucleon-nucleon interaction
• Self-similar extrapolation of nonlinear problems from small-variable to large-variable limit