The variational principle is used to obtain solutions to Schrodinger's
equation for a particle in the Yukawa potential. A Laguerre basis set
extended by an extra function is employed in the calculations. A spec
ial parameter used in the extra function and its relation with the sys
tems energy results in utilizing an auto-coherent scheme. Considerable
improvement seems to be achieved especially in the critical region wh
ere the screening parameter approaches its threshold value.