Consider a particle in a box of length L with one end coinciding with the origin. It isfrequently interesting to know how a system behaves under some disturbance. Thesedisturbances are typically encoded as operators. fd, (æ)Op(x)dx may be interpretedas the probability of finding the system (x) in the eigenfunction , (x) after being actedon by the disturbance Ö.Begin with the system in state n = 1 and compute the probability that the system is foundin some state n 1 under the action of the operator Qx, where Q is just a constant. Inthe case of atomic systems, such operators are known as dipole operators and transitionsinduced by them are called dipole induced transitions. Repeat this problem with theoperator e"/L instead.

Here the system is associated with 1D in potential well, The wave function related to this system is…

Answered: frequently interesting to know how a…

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I solved it but I need help in two parts.For first part, How to show thev formula is a solution of ODE? Second, for the third part, how to show it is bounded because I can not integratw matrix?
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