if we define Z as:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] Z(s)=Tr[exp(-sH)] [/tex]

my 2 questions are..

a) is the trace unique and define the Hamiltonian completely? i mean if

we have 2 Hamiltonians H and K then [tex] Tr[exp(-sH)]\ne Tr[exp(-sK) [/tex]

and if we use the 'Semiclassical approach' then [tex] Z(s)=Tr[exp(-sH)]\sim As^{-1/2}\int_{-\infty}^{\infty}dx exp(-sV(x)) [/tex]

then given Z(s) we could calculate approximately V(x) by solving an integral equation.

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

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!

# DOes the trace determine the Hamiltonian

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