Two crossed 2D troughs create a bound state at their intersection solved via matrix mechanics, finite differences and mode matching, with the latter also yielding a new variational wavefunction of lowest known energy.
Handbook of Mathe- matical Functions with Formulas, Graphs, and Mathemat- ical Tables, 9th Edition
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A simple quantum dot: numerical and variational solutions
Two crossed 2D troughs create a bound state at their intersection solved via matrix mechanics, finite differences and mode matching, with the latter also yielding a new variational wavefunction of lowest known energy.