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What is the potential?

  1. Aug 16, 2005 #1
    let be the next problem: given a particle with mass so [tex]\hbar=(2m)^{0.5} [/tex] then we would have the quantum Hamiltonian:

    [tex]H\phi(x)=E_{n}\phi(x) [/tex] with [tex]H=-D^{2}\phi+V(x)\phi [/tex]

    my question is how i would choose the potential so we have that the energies are the root of the equation [tex]f(x)=0 [/tex]

    i try using the WKB approach to calculate the function:

    [tex]\phi(x)=e^{iS(x)/\hbar} [/tex] with [tex]s^{2}=E_{n}-V(x) [/tex]

    with that i get a functional equation for the potential V(x), my problem is how i introduce the condition that the energies are the roots of f(x)... :frown: :frown:
     
  2. jcsd
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