Question

A. An unnormalized wavefunction for a light atom rotating around a heavy atom to which it is bonded is ψ(φ) = e iφ with 0 ≤ φ ≤ 2π. Normalize this wavefunction.

b.) For the system described in Exercise a, what is the probability of finding the light atom in the volume element dφ at φ = π?

Answer 1

Answer: Your welcome!

Step-by-step explanation:

a.) The normalized wavefunction is ψ(φ) = (1/2π)e iφ. This wavefunction satisfies the normalization condition:

∫ 0 2π |ψ(φ)|2 dφ = 1

b.) The probability of finding the light atom in the volume element dφ at φ = π is (1/2π)|e iπ|2 = 1/2π. This is because the absolute value squared of the wavefunction |ψ(φ)|2 = (1/2π)2, and the integral of the wavefunction over the entire domain is equal to 1. Therefore, the probability of finding the light atom in the volume element dφ at φ = π is (1/2π)|e iπ|2 = 1/2π.