In a paper, I ran into the following definition of the zero point fluctuation of our favorite toy, the harmonic oscillator:
$$x_{ZPF} = \sqrt{\frac{\hbar}{2m\Omega}} $$
where m is its mass and $\Omega$ its natural frequency.
However, when I try to derive it with simple arguments, I think of the equality:
$$E = \frac12 \hbar\Omega=\frac12 m \Omega^2 x_{ZPF}^²$$
(using the energy eigenvalue of the $n=0$ state)
giving me:

$$x_{ZPF} = \sqrt{\frac{\hbar}{m\Omega}} $$
differing from the previous one by a factor $\sqrt2$. I am just puzzled, is it a matter of conventions or is there a fundamental misconception in my (too?) naive derivation? 


Question: Unable to make Zsh not to suggest a fix for an alias
Answer: try


  % unsetopt correct 


I have the spelling correction off by default.

If it works, add it to your .zshrc file.