- #1

MrPhoton

- 2

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## Homework Statement

Show that ∫ ψ

_{1}(x)*ψ

_{2}(x) dx = ∫φ

_{1}(k)*φ

_{2}(k) dk

(Where the integrations are going from -∞ to ∞)

## Homework Equations

1. Plancherel Theorem: ψ(x) = 1/√2π∫φ(k)e

^{ikx}dk ⇔ φ(k) = 1/√2π∫ψ(x)e

^{-ikx}dx

## The Attempt at a Solution

It is clear that Plancherel's theorem must be used to solve this.

We also know by the properties of a wavefunction, that the inner product is orthogonal therefore equal to 0.

Since I know the inner product on the right hand will be 0, I am not quite sure how to show that the left hand side is also equal to the right hand side. (I assume the 1/√2π factors will be removed by the inner product being 0?)