Bounds to expectation values and exponentially decreasing upper bounds to the one-electron density of atoms

Bounds to expectation values of various operators for atomic wavefunctions are derived. For expectation values like ( psi mod e 2 alpha r psi ) they are obtained by means of differential inequalities. Furthermore, a general upper bound to the spherically averaged atomic one-electron density is given. Two special cases are considered: a simple one depending only on the kinetic energy, and an exponentially decreasing bound, in which the estimates for expectation values mentioned above are utilised.