# Problem: A particle detector has a resolution 15% of the width of an infinite square well.What is the chance that the detector will find a particle in the ground state of the square well if the detector is centered on a point one-fourth of the way across the well?

###### FREE Expert Solution

The normalized wave function of a particle in the ground state in an infinite square well:

$\overline{){\mathbf{\phi }}{\mathbf{=}}\sqrt{\frac{\mathbf{2}}{\mathbf{L}}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{\left(}}\frac{\mathbf{\pi }}{\mathbf{L}}{\mathbf{x}}{\mathbf{\right)}}}$

Determining probability:

Where L is the length of the well.

x0 = (1/4)L - (1/2)Resolution = (1/4)L - (1/2)0.15L = 0.175L

x1 = (1/4)L + (1/2)Resolution = (1/4)L + (1/2)0.15L = 0.325L

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###### Problem Details

A particle detector has a resolution 15% of the width of an infinite square well.

What is the chance that the detector will find a particle in the ground state of the square well if the detector is centered on a point one-fourth of the way across the well?