Recursive Construction of the Bosonic Bogoliubov Vacuum State

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.