1. Solve the Schrodinger equation for a particle of mass, m, in a box. The box is modeled as an infinitepotential well that is V, inside the region from 0 < x < L and there is an infinite amount of potentialenergy outside this region. Remark: The only difference between this problem and the one we workedout in a previous lecture is that now the constant potential energy inside the box can be any value,whereas, in the previous lecture, we considered the special case that V, = 0.2abc. Compare the solutions you found in (1) for general V, with those for the case that V, = 0.(a) Does your answer check for that special case?(b) How does the energy levels change?(c) What parts of the solution stay the same and what parts change?3. In view of the parts that stay the same and the parts that change from question (2), are the resultsconsistent with classical physics (yes or no). Note that in classical physics there is no absolute referencepotential energy, because all that affects the dynamics of a particle is the change in potential energy(i.e. forces). As you know, in Newtonian physics it is always possible to add a constant potential energyto the system, and the same dynamics will be observed. How does changing the potential energyreference change the dynamics of the particle within the theory of quantum mechanics? Explain basedon your calculations from (1) and observations in (2).

1) Given: Length of the box is L. Potential inside the box is V0 Calculation: The schematic diagram…

Answered: 1. Solve the Schrodinger equation for a…

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