The Gronwall form of the Schrodinger Equation for Helium

The 1937 paper of Gronwall which concerns an alternative form for the Schrodinger Equation of the 2-electron Helium problem is re-derived in a (hopefully) transparent (possibly pedestrian) manner.

Nitrogen Fertilizer Form and Associated Nitrate Leaching from Cool-Season Lawn Turf

Various N fertilizer sources are available for lawn turf. Few field studies, however, have determined the losses of nitrate (NO3-N) from lawns receiving different formulations of N fertilizers. The objectives of this study were to determine the differences in NO3-N leaching losses among various N fertilizer sources and to ascertain when losses were most likely to occur. The field experiment was set out in a completely random design on a turf typical of the lawns in southern New England. Treatments consisted of four fertilizer sources with fast- and slow-release N formulations: (i) ammonium nitrate (AN), (ii) polymer-coated sulfur-coated urea (PCSCU), (iii) organic product, and (iv) a nonfertilized control. The experiment was conducted across three years and fertilized to supply a total of 147 kg N ha-1 yr-1. Percolate was collected with zero-tension lysimeters. Flow-weighted NO3-N concentrations were 4.6, 0.57, 0.31, and 0.18 mg L-1 for AN, PCSCU, organic, and the control, respectively. After correcting for control losses, average annual NO3-N leaching losses as a percentage of N applied were 16.8% for AN, 1.7% for PCSCU, and 0.6% for organic. Results indicate that NO3-N leaching losses from lawn turf in southern New England occur primarily during the late fall through the early spring. To reduce the threat of NO3-N leaching losses, lawn turf fertilizers should be formulated with a larger percentage of slow-release N than soluble N.