Variational approximation to the spectra of systems with confining potentials

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Abstract
A new simple variational method is proposed. Such a method is wholly rigorous from a formal point of view and it enables us to obtain upper bounds for eigenvalues of physical systems. It is shown that energy eigenvalues calculated in an approximate fashion with trial functions that satisfy the quantum virial theorem, have an identical behavior as that deduced from the WKB method. Numerical results are compared with exact ones.

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