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    Matrix Representation: Hamiltonian of the Infinite Square Well

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    Consider the eigenstates of the infinite square well defined by
    V(x<-a/2) = infinity
    V(-a/2 < x < a/2) = 0
    V (x> a/s) = infinity

    a. If the Hilbert space base-kets for this potential are seen in the attachment. Write down the matrix representation for the Hamiltonian H-hat of the system.
    b. What is the matrix representation for the parity operator P-hat?
    c. Use the matrix representation to verify the commutation relation [H-hat, P-hat]=0

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    Solution Summary

    This solution shows step-by-step calculations to determine the matrix representation for the Hamiltonian H-hat of the system, parity operator P-hat and looks at the commutation relation.