Question

Consider the one-dimensional wave function given by ψ(x)=0 for ∣x∣>aψ(x)=2a1 for −a≤x≤a. Compute the momentum space wave function ϕ(p). b) Compute (Δx)2 and (Δp)2. Is this a minimum uncertainty wave function?

Answer 1

The question deals with computing the momentum space wave function and the uncertainties in position and momentum for a quantum particle, in relation to the Heisenberg Uncertainty Principle.

Step-by-step explanation:

The student is asking about the quantum mechanical problem of finding the momentum space wave function φ(p) for a particle with a given position space wave function ψ(x), and then computing the uncertainties in position (Δx)2 and momentum (Δp)2 to determine if this is a minimum uncertainty wave function. According to the Heisenberg Uncertainty Principle, there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously. The principle suggests that the product of the uncertainties in position and momentum is approximately equal to or greater than the reduced Planck constant (ħ).