1. The problem statement, all variables and given/known data Show that for hydrogen the matrix element <2 0 0|z|2 1 0> = -3a0 where a0 is the Bohr Radius. On account of the non-zero value of this matrix element, when an electric field is applied to a hydrogen atom in its first excited state, the atom's energy is linear in the field strength. 2. Relevant equations Energy of electron: -ħ2/2a02μn2 3. The attempt at a solution <2 0 0| and |2 1 0> are bra and ket states of Hydrogen |n l m> where n is the principle quantum number, l is the orbital number and m is the magnetic number. I think I'm just struggling to work out what the operator z does (does it just point out the z coordinate of the electron?) Any advice on how I can approach this, specifically what matrix is being referred to, would be great.