The physics of inverse square potentials appears in various problems including, pair creation in the presence of an event horizon and black hole decay, optics of Maxwell's fisheye lenses and coherence of sunlight on the earth etc. The quantum mechanics of the inverse square potential is well known for the problem of fall to the centre and the associated ambiguities in the boundary condition. In this talk we demonstrate that the classical field theory of Schwinger pair creation has a hidden scale invariance described by the quantum mechanics of an attractive inverse square potential in the canonically rotated $(Q,P)$ coordinates of the inverted harmonic oscillator. The classical field theory of Schwinger pair creation can be described using an effective Schr\"dinger equation with an inverted harmonic oscillator (IHO) Hamiltonian which exhibits fall to infinity. The vacuum instability in the presence of a static electric field that creates charged pairs is termed as Schwinger pair creation.
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