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Quantum Monte Carlo estimates of the spectrum of rotationally invariantstates of noble gas clusters suggest inter-dimensional degeneracy in $N-1$ and$N+1$ spacial dimensions. We derive this property by mapping the Schr\"odingereigenvalue problem onto an eigenvalue equation in which $D$ appears as acontinuous variable. We discuss implications for quantum Monte Carlo anddimensional scaling methods

Interdimensional degeneracies in van der Waals clusters and quantum Monte Carlo computation of rovibrational states