In Griffiths' Quantum Mechanics, it is mentioned in a problem that

For an unstable particle that spontaneously disintegrates with a lifetime $\tau$, the total probability of finding the particle somewhere should not be constant$(=1)$ but should decrease at an exponential rate given by : $$P(t)=\int_{-\infty}^\infty |\psi(x,t)|^2 dx =e^{-\frac{t}{\tau}}$$

Now the book says that this mathematical result can be proven if we assume that the potential V is a complex quantity, say, $V=V_0-i\gamma$ where $V_0$ and $\gamma$ are real and $\gamma \not =0$.

And I have verified it also, that it can be proved hence.

My question is: What is the physical interpretation of this complex potential and, apart from mathematical reasons, how can I explain the above assumption from a physical aspect?



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