solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看118次
The Hagedorn--Hermite Correspondence. (arXiv:1510.00993v2 [math-ph] UPDATED)
来源于:arXiv
We investigate the relationship between the semiclassical wave packets of
Hagedorn and the Hermite functions by establishing a relationship between their
ladder operators. This Hagedorn--Hermite correspondence provides a unified view
as well as simple proofs of some essential results on the Hagedorn wave
packets. Particularly, we show that Hagedorn's ladder operators are a natural
set of ladder operators obtained from the position and momentum operators using
the symplectic group. This construction reveals an algebraic structure of the
Hagedorn wave packets, and explains the relative simplicity of Hagedorn's
parametrization compared to the rather intricate construction of the
generalized squeezed states. We apply our formulation to show the existence of
minimal uncertainty products for the Hagedorn wave packets, generalizing
Hagedorn's one-dimensional result to multi-dimensions. The Hagedorn--Hermite
correspondence also leads to an alternative derivation of the generating
function for 查看全文>>