The Determination of Energy Levels from Thermodynamic Data. I. The Effect of Experimental Error

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Abstract
The problem of calculating energy levels from thermodynamic data can be reduced to that of inverting the Laplace transform, for which several procedures have been developed. Using the method of Widder, we show that the resultant calculated energy level density function consists of a series of broadened peaks, whereas in the true density the levels are represented by a series of Dirac delta‐functions. Alternatively, if the distribution of the energy levels is specifically assumed to be composed of discrete energies, the calculation reduces to the moment problem. In either case the calculation is shown to have an inherent ``resolving power,'' in that levels within a certain closeness cannot be distinguished as separate. By a generalization of this idea, it is shown that the computation can lead to a knowledge of the over‐all density of energy levels within a given region, but cannot reveal their exact locations.

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