to solve and obtain the potential of a 1-D Hamiltonian we must solve an integral equation

$$ N(E)= A \int_{0}^{E}\frac{V^{-1}(x)}{\sqrt{E-x}}$$

fro a some constant 'A' , then my question is since the approximated espectral fucntion

$$ N(E)= <N(E)>+ \sum_{p.p.o}A_{p}e^{\frac{iS(E)}{\hbar}}+c.c $$

with $ <N(E)>$ meaning the WKB approximation (smooth) to the spectra staircase and p.p.o means summation over the periodic orbits with $ S(E)= \sqrt{2m} l_{p.o}$ the action over the closed orbits , then can i from the Gutzwiller trace formula recover the potential ? this is my ansatz http://vixra.org/pdf/1301.0078v3.pdf which i think is valid at least for one dimension


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.