WM Keck Science
Recently, Schmidt and Schnack [Physica A 260, 479 (1998)], following earlier references, reiterate that the specific heat of N noninteracting bosons in a one-dimensional harmonic well equals that of N noninteracting fermions in the same potential. We show that this peculiar relationship between heat capacities results from a more dramatic equivalence between Bose and Fermi systems. Namely, we prove that the excitations of such Bose and Fermi systems are spectrally equivalent. Two complementary proofs of this equivalence are provided; one based on a combinatoric argument, the other from analysis of the underlying dynamical symmetry group.
Crescimanno, M., and A.S. Landsberg. "Spectral Equivalence of Bosons and Fermions in One-Dimensional Harmonic Potentials." Physical Review A 63.3 (2001): 35601-35603. DOI: 10.1103/PhysRevA.63.035601