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A one-step photoemission analysis is developed, using the exact one-dimensional quantum solution for transmission over and through a triangular barrier presented by Forbes and Deane (2011 Proc. R. Soc. A 467 2927), to evaluate the emission properties of a photocathode in an electron gun. The analysis, which employs transverse momentum conservation in electron emission, includes the physical attributes (density of states and energy-momentum dispersion) of both the bulk band emission states and the recipient vacuum states in its evaluation of the mean transverse energy and relative quantum efficiency of the emitted electrons.