The Hamiltonian operator of a system is H = -(dI dx) + x. Show that Nx exp (-x/2) is an eigenfunction of H and determine the eigenvalue. Also evaluate N by normalization of the function.

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A: Given that:To show that:

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A: Consider the given difference equation.

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A: A matrix is a rectangular representation of elements . There are many types of matrices, like unit…

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Q: 4. y= cje²*+c2xe²*

A: Please see the below picture for detailed solution.

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A: I have used calculator to find eigen values and eigen vectors to avoid lengthy calculation.