# Problem: 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.

###### FREE Expert Solution

(a)

Consider the wave function:

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

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

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###### Problem Details

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.