[@dir49]. In 1905, Einstein used this form of squeeze transformation for the longitudinal and time-like variables. This is known as the Lorentz boost.

In addition, we can consider the transformation of the form $$\pmatrix{x' \cr y'} =
\pmatrix{ 1 & 2\alpha \cr 0 & 1}
\pmatrix{x \cr y} .$$ This transformation shears the system as is shown in Fig. \[ctran11\].

After the squeeze or shear transformation, the wave function of Eq.(\[wf07\]) becomes non-separable, but it can still be written as a series expansion in terms of the oscillator wave functions. It can take the form $$\label{seri22}
\psi(x, y) = \sum_{n,m} A_{n,m} \chi_{n}(x) \chi_{m}(y) ,$$ with $$\sum_{n,m} |A_{n,m}|^2 = 1 ,$$ if $\psi(x,y)$ is normalized, as was the case for the Gaussian function of Eq.(\[gau00\]).

Squeezed Gaussian Function
--------------------------

Under the squeeze along the normal coordinate, the Gaussian form of Eq.(\[gau00\]) becomes $$\label{gau03}
 \psi_{\eta}(x,y) = \frac{1}{\sqrt{\pi}}
              \exp{\left\{-\frac{1}{4}\left[e^{-2\eta}(x + y)^2 +
               e^{2\eta}(x - y)^{2}\right]\right\}} ,$$ which was given in Eq.(\[i01\]). This function is not separable in the $x$ and $y$ variables. These variables are now entangled. We obtain this form by replacing, in the Gaussian function of Eq.(\[gau00\]), the $x$ and $y$ variables by $x'$ and $y'$ respectively, where $$\label{trans22}
  x' = 