The quantum mechanical virial theorem for a general potential $\mathrm{V}(\mathrm{x}, \mathrm{y}, \mathrm{z})$ is given by $\left\langle\mathrm{x} \frac{\partial \mathrm{v}}{\partial \mathrm{x}}+\mathrm{y} \frac{\partial \mathrm{v}}{\partial \mathrm{y}}+\mathrm{z} \frac{\partial \mathrm{v}}{\partial \mathrm{z}}\right\rangle$ where T is the kinetic energy operator and <> indicates expectation value. This leads to the following relation between the expectation value of kinetic energy and potential energy for a quantum mechanical harmonic oscillator problem with potential $\mathrm{V}=\frac{1}{2} \mathrm{k}_{\mathrm{x}} \mathrm{x}^{2}+\frac{1}{2} \mathrm{k}_{\mathrm{y}} \mathrm{y}^{2}+\frac{1}{2} \mathrm{k}_{\mathrm{z}} \mathrm{z}^{2}$