Solutional method for the energies of a parameter-dependent system

which follow from (3) and the semiclassical relation (q,q~) =(qI)(q~); in view of Orland's results for the n= 1 case, the regime for approximate validity of (5) (spanned by the parameters g„y,&, and the quantum numbers of the energy eigenstates) can be expected to transcend the regime. of the latter semiclassical relation if E is required to satisfy E(l. (4). There remains the task of solving —, '(n +n) nonlinear equations (5) in combination with (4) to determine the parameter dependence featured by E. My rigorous mathematical result is the following: A solution to (4) and (5) obtains as and the Hellmann-Feynman equations