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The program LOPT for least-squares optimization of energy levels



Alexander Kramida


The article describes a program that solves the least-squares optimization problem for finding the energy levels of a quantum-mechanical system based on a set of measured energy separations or wavelengths of transitions between those energy levels, as well as determining the Ritz wavelengths of transitions and their uncertainties. The energy levels are determined by solving the matrix equation of the problem, and the uncertainties of the Ritz wavenumbers are determined from the covariance matrix of the problem.
Computer Physics Communications


atomic energy levels, Ritz wavelengths, least-squares optimization


Kramida, A. (2011), The program LOPT for least-squares optimization of energy levels, Computer Physics Communications, [online],, (Accessed May 26, 2024)


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Created February 1, 2011, Updated April 7, 2024