# What does having an imaginary part of potential imply? [duplicate]

In DJ Griffiths' ''Introduction to Quantum Mechanics" to describe an unstable particle that spontaneously disintegrates he assumed an imaginary part in the potential. What does that signify? What is meant by an imaginary potential?

I have added the image of the problem.

• You should also mention the context of the question: from memory, it's one of those cases where you can't derive the continuity equation from the Schrodinger Equation. What do you think that means? Jan 21, 2021 at 8:02
• Jan 21, 2021 at 8:10
• I have solved the given problem but had a conceptual doubt. Jan 21, 2021 at 8:11

Recall that a state evolves as $$|{\psi(t)}\rangle = e^{-i E t/\hbar} |{\psi(0)}\rangle$$. If $$E = E_R + i E_I$$, then $$e^{-i E t/\hbar} = e^{-i E_R t/\hbar} e^{- E_I t/\hbar}$$. The imaginary part of the energy causes exponential decay.