# Derivation of Virial Theorem in Quantum Mechanics

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Solving for Virial Theorem (look at image attached for better symbol representation)

a. In a one-dimensional problem, consider a particle with the Hamiltonian:

H = p^2/2m + V(X)

where: V(C) = lambaX^n

Calculate the commutator [H, XP]. If there exists one or several stationary states |> in the potential V, show that the mean values <T> and <V> of the kinetic and potential energies in these states satisfy the relation: 2<T> = n<V>

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#### Solution Summary

The solution gives proof of virial theorem with full details, detailing the relation between averaged kinetic and potential energy in a quantum mechanical stationary state in a power law potential is considered.

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