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Existence of Bound States in Continuous 0<D<\infty Dimensions

Michael Martin Nieto
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Abstract

In modern fundamental theories there is consideration of higher dimensions, often in the context of what can be written as a Schrödinger equation. Thus, the energetics of bound states in different dimensions is of interest. By considering the quantum square well in continuous $D$ dimensions, it is shown that there is always a bound state for $0 2, a finite-sized well is always needed for there to be a bound state. This size grows like D^2 as D gets large. By adding the proper angular momentum tail a volcano, zero-energy, bound state can be obtained.

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Michael Martin Nieto. 2001-07-25. Existence of Bound States in Continuous 0<D<\infty Dimensions. https://doi.org/10.1016/s0375-9601(01)00827-1

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