Yet another question from question from Griffiths. This time I was able to do the problem, but I’m not able to understand what it means.(adsbygoogle = window.adsbygoogle || []).push({});

Chapter 1, problem 1.15

He talks about unstable particles for which the probability of finding it somewhere is not one, but an exponentially decreasing function of time.

[tex]\int_{-\infty}^{\infty}|\Psi(x,t)|^2dx = e^\frac{-t}{\tau}[/tex] ,

To arrive at this result (in a “crude” way), we assume that the potential energy fucntion has an imaginary part, [itex]\Gamma[/itex].

[tex]V = V_0 - \imath\Gamma[/tex],

where [itex]V_0[/itex] is the true potential energy and [itex]\Gamma[/itex] a positive real constant.

What I don’t understand is the nature of this potential. What’s a complex potential, and does gamma have a physical meaning?

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# Complex potential?

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