Exact solutions of the Schrödinger equation with the position-dependent mass for a hard-core potential. (English) Zbl 1136.81353
Summary: The exact solutions of two-dimensional Schrödinger equation with the position-dependent mass for a hard-core potential are obtained. The eigenvalues related to the position-dependent masses \(\mu _{1}\) and \(\mu _{2}\), the potential well depth \(V_{0}\) and the effective range \(r_{0}\) can be calculated by the boundary condition. We generalize this quantum system to three-dimensional case. The special cases for \(l=0\),1 are studied in detail. For \(l=0\) and \(c=0\), we find that the energy levels will increase with the parameters \(\mu _{2}, V_{0}\) and \(r_{0}\) if \(\mu _{1}>\mu _{2}\).
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
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