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We consider a wave-function approach to the false vacuum decay with gravityand present a new method to calculate the tunneling amplitude under the WKBapproximation. The result agrees with the one obtained by the Euclideanpath-integral method, but gives a much clearer interpretation of an instanton(Euclidean bounce solution) that dominates the path integral. In particular,our method is fully capable of dealing with the case of a thick wall with theradius of the bubble comparable to the radius of the instanton, thus surpassingthe path-integral method whose use can be justified only in the thin-wall andsmall bubble radius limit. The calculation is done by matching two WKB wavefunctions, one with the final state and another with the initial state, withthe wave function in the region where the scale factor of the metric issufficiently small compared with the inverse of the typical energy scale of thefield potential at the tunneling. The relation of the boundary condition on ourwave function for the false vacuum decay with Hartle-Hawking's no-boundaryboundary condition and Vilenkin's tunneling boundary condition on the wavefunction of the universe is also discussed.Comment: 11 pages, 5 figures, submitted to PR

False vacuum decay with gravity in the non-thin-wall limit