Physical chem test

Anonymous
timer Asked: Nov 18th, 2018
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1. a. Consider a particle in a one dimensional box with infinite potential energy walls. Write the Schrodinger equation in as much detail as possible assuming that there is no potential energy contribution to the Hamiltonian. (5 pts.) b. Consider the particle in the 3rd energy state (with 1st being the lowest in energy). Plot the probability density function for this state and specify where in the box is the particle most likely to be. Give a general expression for the maxima in the probability density function in a state n. (5 pts.) c. Consider the three states of the particle in this box that have the lowest energy. For each of these three states, specify if there are one or more wave functions that describe the particle in the respective state? (5 pts.) d. The wave function for the particle in the box has the general form: ⎛ 2π ⎞ Ψ (x ) = A × sin ⎜ 2mE x ⎟ h ⎝ ⎠ ! Use the boundary condition at the limit of the box x = a to determine the formula for the energy of the particle in the box as a function of n, h, m and a. (10 pts.)

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rahul46
School: UIUC

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Anonymous
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