HIGHER-ORDER LEVINSON THEOREMS AND THE HIGH-TEMPERATURE EXPANSION OF THE PARTITION-FUNCTION

Higher-order two-body Levinson's theorems are proved for the class of potentials V ∈ L1 ∩ L2 in terms of the energy moments of the trace of the time-delay operator. If V is smooth, the correction terms appearing in these trace relations are Korteweg-de Vries-type invariants. These theorems are used to derive the high-temperature expansion of the quantum mechanical grand partition function, explicitly showing the cancellation between the bound-state contributions and scattering contributions. © 1979.