I need to know the s-wave resonances of the central potential $V(r)=-c^2(r+1/r)^2, c\in \Re$. Here we have a well attached to a barrier so we expect quantized quasibound/ metastable/ resonant states (Gamov's states). The reduced radial Schoedinger equation $$u''(r)+(k^2+ c^2(r+1/r)^2] u(r)=0,~ r \in (0,\infty)$$ ($2m=1=\hbar^2$) for this potential is solvable in terms of confluent hypergeometric and Laguarre functions. However, finding a solution which vanishes at $r=0$ and behaves as (Gamov's) out-going wave asymptotically could be challenging. I wonder, if the analytic complex eigenvalues of the type $E_n-i\Gamma_n/2$ are already known for this potential. Any information or Ref. is welcome.


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.