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Commutation and Completeness in 1D Hamiltonian

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I need some help with this Hamiltonian question:
Consider the Hamiltonian H of a particle in a one-dimensional problem defined by:
H = 1/2mp^2 + V(X)

Where X and P are operators defined in E of chapter 2 and which satisfy the relation: [X, P] ih. The eigenvectors of H are denoted in the attached file, as well as the question a, b.

Reference: Cohen Quantum Mechanics

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The solutions shows, in detail, how to arrive at the required relationships between the momentum and position operators for a particle in some 1D Hamiltonian.

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