LA - UR - 01 - 3190 Existence of Bound States in Continuous 0 < D < ∞ Dimensions
نویسنده
چکیده
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 < D ≤ 2. This binding is complete for D → 0 and exponentially small for D → 2−. For D > 2, a finite-sized well is always needed for there to be a bound state. This size grows like D as D gets large. By adding the proper angular momentum tail a volcano, zero-energy, bound state can be obtained.
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Existence of Bound States in Continuous 0 < D < ∞ Dimensions
In modern fundamental theories, there often 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 < D ≤ 2. This binding is complete for D → 0 an...
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