- #1
MrPhoton
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Homework Statement
Show that ∫ ψ1(x)*ψ2(x) dx = ∫φ1(k)*φ2(k) dk
(Where the integrations are going from -∞ to ∞)
Homework Equations
1. Plancherel Theorem: ψ(x) = 1/√2π∫φ(k)eikx 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?)