I will present a definition and some important properties of the bosonic operators for back-stable Schubert polynomials. The operators act on the left weak Bruhat order (divided difference and Monk’s rule use the right side action on permutations in my notations). These operators with an extra condition give sufficiently enough linear equations for the structure constants of flag varieties. In particular, they provide a recurrent formula for the structure constants. In some special cases it is easy to check the positivity of the structure constants using this formula, examples will be presented. One of the advantages of our method is that we do not need to use formulas for Schubert polynomials and back-stable Schubert polynomials. Nevertheless if time permits, I will also show how to establish the pipe dreams formula using these operators.