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## \sigma_{x}\sigma_{p} \geq \frac{\hbar}{2},##

where ##x,p## are the usual quantum operators and ##\hbar## the Planck constant divided by ##2\pi##. If I understood correctly, Gaussian states that are solution of the quantum harmonic oscillator minimize the uncertainty principle with the equality. The question is what happen for the other Gaussian states? It is true for every Gaussian state? For example considering a Gaussian state of the form ## \psi=Ce^{-\lambda x^2}## (with ##C## constant and ##\lambda## a real parameter) it is the inequality true for every ##\lambda##?

Thank you in advance for all answer to by doubt.

Ssnow