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In class, we are discussing a free particle trapped inside the box. Keeping this discussion in...

In class, we are discussing a free particle trapped inside the box. Keeping this discussion in mind, please answer the following questions. (a) Calculate the probability of finding the particle in the first one third of the box (0 to a/3). The particle is residing in the first excited state. (b) Show that the ground state wavefunction is orthogonal to the first excited state wavefunction. (c) Uncertainty is defined as the square root of variance ( a 2 = - 2 ). Calculate the uncertainty in momentum and position for the particle in a box. (SHOW your work)

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