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A question about the adding of potential in Schrodinger equation

  1. Mar 22, 2005 #1
    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. jcsd
  3. Mar 22, 2005 #2

    dextercioby

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    Science Advisor
    Homework Helper

    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.
     
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