Limits of Error for the Electron Density, Spin Density, and Atomic Form Factor in Quantum-Mechanical Calculations

Explicit formulas are given for the limits of error at an arbitrary point in the electron density, spin density, and form factor derived from an approximate wave function. In the derivation extensive use is being made of some previous results by Kinoshita. The main treatment is preceded by a short discussion of some of the more mathematical aspects of the problem, and a simple numerical example is given in the last paragraph.