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Reconstruction of potential V(x)

  1. Aug 21, 2009 #1
    the idea is, let us suppose we know the trace

    [tex] Tr(h(\hat H ))= \sum_{n=0}^{\infty}h(E_n ) [/tex]

    here 'h' can be a real or complex exponential of the form exp(-ax) and 'H' is the usual Hamiltonian operator

    [tex] H=p^2 + V(x) [/tex]

    what information about the spectrum of Hamiltonian would i need in order to obtain V(x) ??

    for example: for the Harmonic Oscillator in Planck's unit so h=1 and w=1 i have that

    [tex] \sum _{n=0}^{\infty} exp(-s(n+1/2))= \frac{exp(-s/2)}{1-exp(-s)} [/tex]

    then from the expression above could i conclude that potential goes like [tex] V(x)=ax^{2} [/tex]
  2. jcsd
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