Abstract
In this paper, the Schrödinger equation in the presence of a screened Coulomb potential and a uniform field is analysed using matched asymptotic expansions. When the cup well potential has a very short range, approximate analytical expressions for the energy levels and the lifetime of the system are found. The results are compared with those described in the literature. This paper may be helpful for undergraduate and graduate students in physics as an introductory problem in the application of asymptotic matching applied to quantum mechanics.
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