= \left[\frac{1}{\sqrt{\pi}2^m m!}\right]^{1/2}
              H_{m}(y) \exp{\left(\frac{-y^{2}}{2}\right)} ,$$ and construct the function $$\label{wf07}
\psi^{n,m}(x,y) =\left[\chi_{n}(x)\right]\left[\chi_{m}(y)\right].$$ This form is clearly separable in the $x$ and $y$ variables. If $n$ and $m$ are zero, the wave function becomes $$\label{gau00}
 \psi^{0,0}(x,y) = \frac{1}{\sqrt{\pi}}
              \exp{\left\{-\frac{1}{2}\left(x^2 + y^2\right)\right\}}.$$ Under the coordinate rotation $$\label{trans11}
 \pmatrix{x' \cr y'} = \pmatrix{\cos\theta & -\sin\theta \cr
      \sin\theta & \cos\theta}  \pmatrix{x \cr y}$$ this function remains separable. This rotation is illustrated in Fig. \[ctran11\]. This is a transformation very familiar to us.

We can next consider the scale transformation of the form $$\label{sq03}
 \pmatrix{x' \cr y'} = \pmatrix{e^{\eta} & 0 \cr
      0 & e^{-\eta}} \pmatrix{x \cr y} .$$ This scale transformation is also illustrated in Fig. \[ctran11\]. This area-preserving transformation is known as the squeeze. Under this transformation, the Gaussian function is still separable.

If the direction of the squeeze is rotated by $45^o$, the transformation becomes the diagonal transformation of Eq.(\[sq02\]). Indeed, this is a squeeze in the normal coordinate system. This form of squeeze is most commonly used for squeezed states of light as well as the subject of entanglements. It is important to note that, in terms of the $x$ and $y,$ variables, this transformation can be written as Eq.(\[sq01\]) 