Uncertainty of energy in a quantum harmonic oscillator

[bobred]

Homework Statement

Find the uncertainty of the kinetic energy of a quantum harmonic oscillator in the ground state, using

\left\langle p^2_x \right\rangle = \displaystyle\frac{\hbar^2}{2a^2} and
\left\langle p^4_x \right\rangle = \displaystyle\frac{3\hbar^2}{4a^2}

Homework Equations

\Delta E_{kin}=\sqrt{\left\langle E^2_{kin} \right\rangle - \left\langle E_{kin} \right\rangle^2}

\left\langle E_{kin} \right\rangle = \displaystyle\frac{\left\langle p^2_x \right\rangle}{2m}

The Attempt at a Solution

With \left\langle E_{kin} \right\rangle^2 I have no problem with but am I valid in saying

\left\langle E^2_{kin} \right\rangle = \displaystyle\frac{\left\langle p^4_x \right\rangle}{4m^2}?

 

[DrClaude]

am I valid in saying

\left\langle E^2_{kin} \right\rangle = \displaystyle\frac{\left\langle p^4_x \right\rangle}{4m^2}?

Yes.