Bound states and critical behavior of the Yukawa potential. (English) Zbl 1101.81053
Summary: We investigate the bound states of the Yukawa potential \(V(r)=-\lambda\exp(-\alpha r)/r\), using different algorithms: solving the Schrödinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical \(\alpha=\alpha_C\), above which no bound state exists. We study the relation between \(\alpha_C\) and \(\lambda\) for various angular momentum quantum number \(l\), and find in atomic units, \(\alpha_C(l)=\lambda[A_1\exp(-l/B_1)+A_2\exp(-l/B_2)]\), with \(A_1=1.020(18)\), \(B_1=0.443(14)\), \(A_2=0.170(17)\), and \(B_2= 2.490(180)\).
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81-08 | Computational methods for problems pertaining to quantum theory |
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