# Is this solvable?

1. Apr 5, 2006

### eljose

I would like to know if the functional integral:

$$D[\phi]e^{iS[\phi]/\hbar$$ (1)

where S is the classical action of a system of a Lagrangian with a potential in the form:

$$V=\sum_{n}\delta(x-n)$$ n=0,1,2,3,4,5,6,...........

The Schroedinguer equation if the sum is finite can be transformed into a solvable "integral equation"..but i would like to know if the functional is exactly integrable,...by the way i would like to know how Feynmann obtained the Schroedinguer equation by calculating the infinite integral (1) for S the action:

$$S=\int_{a}^{b}dt\alpha{(dx/dt)^{2}}$$

then this integral in (1) would be a Gaussian and could be calculated exactly but how you derive Schroedinguer equation?..thanks.

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