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1

Let me continue on from BeastRaban's exposition: In 1866, Mehler figured out how to carry out the sum for the $u_n(x)$ eigenfunctions of the quantum harmonic oscillator, Hermite polynomials, adding them all to an elegant and compact eponymous Mehler kernel, or equivalently. The Green's function (propagator) for the quantum harmonic oscillator is then: $$ ...


2

There is no problem, you just have to go back to the definition of the terms in the LSZ formula to see that $\langle p \vert S \vert q \rangle\vert_\text{connected}$ is indeed just zero for the 1-particle process $p\to q$, and it is only this connected piece that appears in the LSZ formula you are trying to use to compute this amplitude. (In the notes you ...



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