  Applying the Jacobi method of second variation to the Bianchi IX system in
Misner variables $(\alpha, \beta_+, \beta_-)$, we specialize to the Taub space
background $(\beta_- = 0)$ and obtain the governing equations for linearized
homogeneous perturbations $(\alpha', \beta_+', \beta_-')$ thereabout. Employing
a canonical transformation, we isolate two decoupled gauge-invariant linearized
variables ($\beta_-'$ and $Q_+' = p_+ \alpha' + p_\alpha \beta_+'$), together
with their conjugate momenta and linearized Hamiltonians. These two linearized
Hamiltonians are of time-dependent harmonic oscillator form, and we quantize
them to get time-dependent Schr\"{o}dinger equations. For the case of $Q_+'$,
we are able to solve for the discrete solutions and the exact quantum squeezed
states.
