Tunneling is a hallmark phenomenon in quantum mechanics. While the classical trajectory cannot enter regions that are forbidden by energy conservation, the wave function can (without violating the conservation law). I will review how to calculate the probability flux for tunneling from resonant-state (Gamov-Siegert) wave function solutions to the Schrödinger equation. On the other hand, there is Coleman and Callan’s path-integral method for computing the rates. I will present recent results on how to establish a direct connection between these two methods. These rely on extending the Schrödinger problem to the complex
plane.
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