# Particle in a Box

A particle is constrained to lie along a one-dimensional line segment between 0 and a. The probability of finding the particle along this line segment is seen in attached file.

A. Find the proportionality constant, ie., normalize the function.

B. Calculate the expectation values of X and X^2 for n=1 and n=2.

C. Find the Variance and standard deviation for a particle with n=1 and 2.

D. What is the probability of finding the particle between 0 and a/2 when n=1 and 2.

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#### Solution Preview

Please find the attached solution.

A particle is constrained to lie along a one-dimensional line segment between 0 and a. The probability of finding the particle along this line segment is :

A. Find the proportionality constant, i.e., normalize the function.

B. Calculate the expectation values of X and X^2 for n=1 and n=2.

C. Find the Variance and standard deviation for a particle with n=1 ...

#### Solution Summary

This in-depth solution contains step-by-step calculations with explanations to determine the proportionality constant, expectation values, variance, standard deviation and probability. All formulas and workings are shown in structured manner.