Mathematical Definition
The most general wave function that satisfies the identity above is the squeezed coherent state (we work in units with )
where are constants (a normalization constant, the center of the wavepacket, its width, and its average momentum). The new feature relative to a coherent state is the free value of the width, which is the reason why the state is called "squeezed".
The squeezed state above is an eigenstate of a linear operator
and the corresponding eigenvalue equals . In this sense, it is a generalization of the ground state as well as the coherent state.
Read more about this topic: Squeezed Coherent State
Famous quotes containing the words mathematical and/or definition:
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)