Abstract
An explicit expression for the Laplace transform of a Lorentzian function is applied to evaluate the contribution to the canonical partition function of ideal-gas molecules stemming from resonances. This formula can be used instead of numerical integration. A discussion of potential errors in replacing this contribution by the conventional formula for the Boltzmann weight is given. When generalised to the complex plane, the known expression is shown to be discontinuous and a new formulation is proposed that removes the discontinuity. As a result, an explicit expression is obtained for the Fourier transform of a Lorentzian function that is truncated at a lower energy bound.
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