**(a)**

Consider the wave function:

$\mathit{\Psi}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}\mathit{A}{\mathit{e}}^{\mathbf{\u2013}\mathbf{\alpha}{\mathbf{x}}^{\mathbf{2}}}$

If the value of α is increased, the width of the wave function decreases.

A particle is described by a wave function Ψ(x) = Ae^{–αx2}, where A and α are real, positive constants. If the value of a is increased, what effect does this have on (a) the particle's uncertainty in position and (b) the particle's uncertainty in momentum? Explain your answers.

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