Can you help me with this problem from Sakurai:

A particle of mass m in one dimension is bound to a fixed center by an attractive delta-function potential:

$$V(x) ~= ~-a\delta(x) , \qquad a>0.$$

At $t = 0$, the potential is suddenly switched off (that is, $V = 0$ for $t > 0$). Find the wave function for $t > 0$.

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    $\begingroup$ Is there a conceptual question hidden in there? $\endgroup$ – Alfred Centauri Jun 14 '13 at 20:17
  • $\begingroup$ No, it's a problem. I think that I may solve it using the free - particle propagator, am I right? $\endgroup$ – Surreal Jun 14 '13 at 20:27
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    $\begingroup$ Hi Surreal, and welcome to Physics Stack Exchange! This is a site for conceptual questions about physics, not general homework help. If you can edit your question to ask about the specific physics concept that is giving you trouble, I'll be happy to reopen it. See our FAQ and homework policy for more information. $\endgroup$ – David Z Jun 14 '13 at 23:24

So you know the wavefunction when the delta function is on. Project the plane wave basis onto the wavefunction (when delta is on) and turn on time dependence.


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