In: Physics
Asume the wave function Ψ(x) = A/(x²+a²) whith x real, A and a constants
a) find the normalized wave function Φ(p) un the momentum space associated to Ψ(x)
b) use Φ(p) yo compute the expected values for p, p², and σ_p
c) verify if this state fulfills the Heisenberg uncertainty principle
All the parts have been attempted. The expectation values of <x> and <x^2>, though not asked in the question, are important to prove the uncertainty principle. Thus, they have been discussed in brief and the integrals involved can be solved very easily.