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:

φ=2Lsin(πLx)

Determining probability:

P=φ2dx=x0x1(2Lsin(πL)x)2=2Lx0x112(1 - cos(2πLx))=1L(x1-L2πsin(2πLx1) - x0 + L2πsin(2πLx0)

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

92% (120 ratings)
View Complete Written Solution
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?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Quantum Mechanics concept. You can view video lessons to learn Quantum Mechanics. Or if you need more Quantum Mechanics practice, you can also practice Quantum Mechanics practice problems.