  Analytical approximations for ${< \phi^2 >}$ and ${< T^{\mu}_{\nu} >}$ of a
quantized scalar field in static spherically symmetric spacetimes are obtained.
The field is assumed to be both massive and massless, with an arbitrary
coupling $\xi$ to the scalar curvature, and in a zero temperature vacuum state.
The expressions for ${< \phi^2 >}$ and ${< T^{\mu}_{\nu} >}$ are divided into
low- and high-frequency parts. The contributions of the high-frequency modes to
these quantities are calculated for an arbitrary quantum state. As an example,
the low-frequency contributions to ${< \phi^2 >}$ and ${< T^{\mu}_{\nu} >}$ are
calculated in asymptotically flat spacetimes in a quantum state corresponding
to the Minkowski vacuum (Boulware quantum state). The limits of the
applicability of these approximations are discussed.
