Generalized Squeeze Equation and Its Symmetry

摘要

I study the solutions, symmetry, and the map under time inversion (t - 1/t) of the following generalized squeeze equation (GSQE)Sigma k=. n, mu = .. t -. n k= 1. 2. x2 k -. t2 m r= 1. 2. p2r u( t, xk, pr) = 0, which is a formal generalization of the squeeze equation SQE,. Q = . t - 1 4. x2 + 1 4t2. p2 Q( t, x, p) = 0.determine the Lie symmetry algebra g(n,m) of the GSQE, which yields a deeper understanding of the Lie symmetry algebra g(n,0) of the n-dimensional heat equation. I introduced the parameter to obtain an internal contraction' of so(n,m) to iso. n, mu = .. t -. n k= 1. 2. x2 k -. t2 m r= 1. 2. p2r u( t, xk, pr) = 0, which is a formal generalization of the squeeze equation SQE,. Q = . t - 1 4. x2 + 1 4t2. p2 Q( t, x, p) = 0.(n,m), similar to that of the hydrogen atom.