Evolution equations invariant under two-dimensional space-time Schrodinger group

1993
13 pages
Published in:
  • J.Math.Phys. 34 (1993) 558-570

Citations per year

199520012007201320193012
Abstract: (AIP)
The most general second order evolution equation ψ t +F(x,t,ψψ*,ψ x ,ψ x *,ψ xx , ψ xx *)=0, invariant under the Galilei, Galilei‐similitude, and Schrödinger groups in two dimensions, is constructed. A preliminary step is a classification of all possible realizations of the corresponding Lie algebras of vector fields in R2×C parametrized by x, t, ψ, and ψ*. Applications of this study include the investigation of nonlinear alternatives to quantum mechanics and nonrelativistic classical field theories. Among the Schrödinger invariant equations, in particular, are found integrable equations, linearizable by contact transformations.
  • Schroedinger equation
  • group theory: Schroedinger
  • dimension: 2
  • invariance: Galilei
  • field theory: vector
  • algebra: Lie
  • quantum mechanics
  • nonrelativistic
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