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I was trying to find out the propagator for the inverted SHO (something like tachyon oscilltor) and turns out that it remains unitary only for very short times. Which didnt make much sense to me. I tried looking at the usual SHO propagator, and that too seems to be not Unitary!!! ( I tried checking it by doing ∫U(x,x') U*(x',x'') dx' and see if that equals the dirac delta. I found that it blows up at x=x'' as it should but for x ≠ x' it is not zero)

Ofcourse I might(should) be making a mistake somewhere. But even an initial glance at the propagator for usual SHO would hint that there is something it fishy, since it contains terms like sin(ωt).

Thanks

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# Propagator for inverted harmonic potential.

Can you offer guidance or do you also need help?

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