Numerically exact solution to QRM for E#0 (8+0 QHC et al. arXiv: 1007. 1747 Transformation(w=1) A=a+a, a=8 B=a-a AT A H g △/2BB-g2+ Ansatz for the wavefunction A a+a A ∑。"(-1)an|n) -e m-g ∑ mg+1-2.DB, aguerre polynomia o For strong coupling or highly excited states, much better than exact diagonalization in a-spaceA a , B a   = + = − Transformation (ω=1)  = g 2 2 2 2 A A g H B B g   + +   − + − =     − − + ( ) 0 0 1 tr tr N n n A N n n n B c n d n  = =   =     −     2 2 2 2 m mn n m n m mn n m n m g c D d Ec m g d D c Ed     − − − =       − + − =       Ansatz for the wavefunction Numerically exact solution to QRM for ε≠0 (δΦ≠0) QHC et al, arXiv: 1007.1747 ( ) ( ) 1 2 2 0 0 ! ! 0 0 n n A A A g ga A a A a n n n e  + + + − − + = = = ( ) ( ) ( ) 2 2 1 2 ! 2 exp 2 (4 ) ! m mn B A n m n m B m A D m n m m n g g L g n − −  = − = Laguerre polynomial ◇ For strong coupling or highly excited states, much better than exact diagonalization in a-space