I study the solutions, symmetry, and the map under time inversion (t ↦ 1/t) of the following generalized squeeze equation (GSQE)♡n,mu≡[∂∂t−k(∑k=1n∂2∂xk2−γt2∑r=1m∂2∂pr2)]u(t,xk,pr)=0,which is a formal generalization of the squeeze equation SQE,♡Q≡[∂t−14∂x2+14t2∂p2]Q(t,x,p)=0.I 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 γ to obtain an ‘internal contraction’ of so(n,m) to iso(n,m), similar to that of the hydrogen atom.
|Number of pages||4|
|Journal||Physics of Atomic Nuclei|
|State||Published - 1 Nov 2018|
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics