 Power-law quantum virial theorem

For a bound stationary state in a homogeneous potential $V(\lambda x)={\lambda }^{n}V(x)$, scaling a normalized wavefunction gives stationarity of ${\lambda }^2⟨T⟩+{\lambda }^{-n}⟨V⟩$ at $\lambda =1$. Hence $2⟨T⟩=n⟨V⟩$.