Abstract
A systematic ħ-expansion of the regulated Witten index Δ(β) in one and two-dimensional SUSY quantum mechanics reveals that the lowest order ħ-term is nonzero, and all terms to at least the next four orders vanish. In one dimension, this lowest order term yields the well-known exact quantum result for an arbitrary superpotential. For the Pauli Hamiltonian with an arbitrary vector potential in two-dimensions, we find the new result that the semiclassical Δ(β) is β-independent and is equal to the number of magnetic flux lines.
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