1. Mar 22, 2005

wenty

If
H1=P^2/2m+V1(x), H2=P^2/2m+V2(x), H=P^2/2m+V1(x)+V2(x)
and
H1 f1_i(x)=E1_i*f1_i(x),
H2 f2_j(x)=E2_j*f2_j(x),
H f_k(x)=E_k*f_k(x)

Is there any relation between f1_i(x),f2_j(x),f_k(x)?Can we express f_k(x) in terms of f1_i(x) and f2_j(x)?

2. Mar 22, 2005

dextercioby

Not really.U've actually given a very abstract problem.In a QM description in the Schrödinger picture,it is essential to know the potential.Just then,after having specified the physical system (its interactions),u can apply the "machinery" of QM.

One of the most important mathematical theorems in QM regards CSCO-s.If your operators form a CSCO,then u can apply it.

Daniel.