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In this paper, we use the WKB approximation method to approximately solve adeformed 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 within 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 WKBsolutions, the WKB connection formulas through a turning point, the deformedBohr--Sommerfeld quantization rule, and the deformed tunneling rate formulathrough a potential barrier. Several examples of applying the WKB approximationto the deformed quantum mechanics are investigated. In particular, we calculatethe bound states of the P\"{o}schl-Teller potential and estimate the effects ofquantum gravity on the quasinormal modes of a Schwarzschild black hole.Moreover, the area quantum of the black hole is considered via Bohr'scorrespondence principle. Finally, the WKB solutions of the deformedWheeler--DeWitt equation for a closed Friedmann universe with a scalar fieldare obtained, and the effects of quantum gravity on the probability ofsufficient inflation is discussed in the context of the tunneling proposal.

WKB Approximation for a Deformed Schrodinger-like Equation and its Applications to Quasinormal Modes of Black Holes and Quantum Cosmology