the idea is, let us suppose we know the trace(adsbygoogle = window.adsbygoogle || []).push({});

[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]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Reconstruction of potential V(x)

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**