  In this paper, we use the WKB approximation method to approximately solve a
deformed Schrodinger-like differential equation: $\left[ -\hbar^{2}
\partial_{\xi}^{2}g^{2}\left( -i\hbar\alpha\partial_{\xi}\right) -p^{2}\left(
\xi\right) \right] \psi\left( \xi\right) =0$, which are frequently dealt with
in various effective models of quantum gravity, where the parameter $\alpha$
characterizes effects of quantum gravity. For an arbitrary function $g\left(
x\right) $ satisfying several properties proposed in the paper, we find the WKB
solutions, the WKB connection formulas through a turning point, the deformed
Bohr--Sommerfeld quantization rule, and the deformed tunneling rate formula
through a potential barrier. Several examples of applying the WKB approximation
to the deformed quantum mechanics are investigated. In particular, we calculate
the bound states of the P\"{o}schl-Teller potential and estimate the effects of
quantum gravity on the quasinormal modes of a Schwarzschild black hole.
Moreover, the area quantum of the black hole is considered via Bohr's
correspondence principle. Finally, the WKB solutions of the deformed
Wheeler--DeWitt equation for a closed Friedmann universe with a scalar field
are obtained, and the effects of quantum gravity on the probability of
sufficient inflation is discussed in the context of the tunneling proposal.

General Relativity and Quantum Cosmology