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We review the Schr\"odinger picture of field theory in curved spacetime andusing this formalism, the power spectrum of massive non-interacting, minimallycoupled scalars in a fixed de Sitter background is obtained. To calculate theN-point function in Schr\"odinger field theory, the "in-in" formalism isextended in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe. Wecompute the three-point function for primordial scalar field fluctuation in thesingle field inflation by this in-in formalism. The results are the same as thethree-point function in the Heisenberg picture.

Schr\"odinger field theory in curved spacetime: In-In formalism and three-point function for inflationary background