Editing Squeezed coherent state (section)

==Mathematical definition==
[[File:QHO-coherent3-amplitudesqueezed2dB-animation-color.gif|thumb|right|300px|Animated position-wavefunction of a 2dB amplitude-squeezed coherent state of α=3.]]
The most general [[wave function]] that satisfies the identity above is the '''squeezed coherent state''' (we work in units with <math>\hbar=1</math>)

:<math>\psi(x) = C\,\exp\left(-\frac{(x-x_0)^2}{2 w_0^2} + i p_0 x\right)</math>

where <math>C,x_0,w_0,p_0</math> are constants (a normalization constant, the center of the [[wavepacket]], its width, and the expectation value of its [[momentum]]). The new feature relative to a [[coherent state]] is the free value of the width <math>w_0</math>, which is the reason why the state is called "squeezed".

The squeezed state above is an [[eigenstate]] of a linear operator

:<math> \hat x + i\hat p w_0^2</math>

and the corresponding [[eigenvalue]] equals <math>x_0+ip_0 w_0^2</math>. In this sense, it is a generalization of the ground state as well as the coherent state.