Simple example illustrating the different parametrizations of the Mo/ller operator

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Abstract
Various energy and convergence factor parametrizations of the Mo/ller operator are discussed. These can usually be applied to eigenstates of the free Hamiltonian, in contrast to the Mo/ller operator itself, which is only correctly defined in Hilbert space. Formal differences of the parametrized operators are exemplified in one dimension using a particular separable potential for which all computations can be carried out analytically. The behavior of the energy parametrized operators are contrasted when the convergence parameter is taken to zero and it is shown how the parametrized operators may be consistently used if a proper interpretation of the formulas is maintained. The second virial coefficient is also examined for the particular potential and it is shown how the Mo/ller operator can be used in its evaluation.

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