Unusual bound or localized states

Abstract

We summarize unusual bound or localized states in quantum mechanics. Our guide through these intriguing phenomena is the classical physics of the upside-down pendulum. Taking advantage of the analogy between the corresponding Newton's equation of motion and the time-independent Schrödinger equation, we discuss the zero-energy ground state in a three-dimensional, spatially oscillating, potential. Moreover, we focus on the effect of the attractive quantum anti-centrifugal potential that only occurs in a two-dimensional situation.

11 pages, 4 figures

Cited by in corpus (5)

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• Bound States in Sharply Bent Waveguides: Analytical and Experimental Approach
• Huygens' principle, the free Schrodinger particle and the quantum anti-centrifugal force
• Dimensional enhancement of kinetic energies
• The granularity of weakly occupied bosonic fields beyond the local density approximation