The derivation of the exact wave function for Boson Bogoliubov transformation

Phan Thành Nam, Marcin Napiórkowski, Jan Philip Solovej

Iacopo Carusotto, Yvan Castin

Raoelina Andriambololona

Wensen Liu

In this paper,the exact expressions of the evolution operator and wave function are obtained by means of the combination of the inhomogeneous Bogoliubov transformation(IBT) and the evolution equation associated with a su(1,1)h(4).As a model example,we have got the exact expressions of the evolution operator and Schrdinger wave function of the driven time-dependent harmonic oscillator.These results agree well with those derived in general refrences,but the present method is more simple and definite.what's more,it is easily extended to other su(1,1)h(4) quantum system

Wolfgang Witschel

D. Portes, Marcos O Pinho, Hilário Rodrigues

Abstract: In this work we derive a novel procedure for obtaining the bosonic Bogoliubov vacuum states by using a recursive scheme. The vacuum state for the new creation and annihilation operators is explicitly constructed in terms of the number states of the old operators, which are connected by a Bogoliubov transformation. The coefficients of the ground state in Fock basis are thus obtained as exclusive functions of the parameters of the Bogoliubov transformations.