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.

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.

... treat electrons in conjugated pi systems as particles in one ... Now that we have the box length, the wavefunctions and ... and m is the mass of the particle (here, an ...

Quantum Mechanics: Combination of the particle in a box and the Harmonic oscillator. Please read the attached file for complete description of the problem. ...

... of this system if the box contains only one particle? (b) What is the partition function of this system if the box contains two distinguishable particles? ...

... In a box model, the maximum distance to transport particle across a city is shown as D. If the approximate length of one side is 40 miles, width is 28 miles ...

... assumptions, the "residence time" of pollution particles is governed ... of the city gets displaced (moved) from the box. ... we follow the journey of a particle as it ...

... Neutron (particles that have neither positive or negative charge; in the nucleus of a cell). (Perhaps- Label according to position of identification boxes (from ...

... same as same as the applied force to the bigger box so that the two boxes keep up ... 12 The vertical motion of the particle is independent of the horizontal motion ...