  We revisit the path integral description of quantum tunneling and show how it
can be generalized to excited states. For clarity, we focus on the simple toy
model of a point particle in a double-well potential, for which we perform all
steps explicitly. Instead of performing the familiar Wick rotation from
physical to imaginary time - which is inconsistent with the requisite boundary
conditions when treating tunneling from excited states - we regularize the path
integral by adding an infinitesimal complex contribution to the Hamiltonian,
while keeping time strictly real. We find that this gives rise to a complex
stationary-phase solution, in agreement with recent insights from
Picard-Lefshitz theory. We then show that there exists a class of analytic
solutions for the corresponding equations of motion, which can be made to match
the appropriate boundary conditions in the physically relevant limits of a
vanishing regulator and an infinite physical time. We provide a detailed
discussion of this non-trivial limit. We find that, for systems without an
explicit time-dependence, our approach reproduces the picture of an
instanton-like solution defined on a finite Euclidean-time interval. Lastly, we
discuss the generalization of our approach to broader classes of systems, for
which it serves as a reliable framework for high-precision calculations.
