1. The problem statement, all variables and given/known data Prove that Neither <xp>=∫ψ* x(ħ/i)(∂/∂x) ψ dx nor <xp>=∫ψ* x(ħ/i)(∂/∂x)xψ dx is acceptable because both lead to imaginary value.Show that <xp>=∫ψ* x(ħ/i)(∂/∂x) ψ dx + ∫ψ* x(ħ/i)(∂/∂x)xψ dx leads to real value.Does <xp>=<x><p> ? 2. Relevant equations 3. The attempt at a solution Taking * of proposed <xp>=∫ψ* x(ħ/i)(∂/∂x) ψ dx and carrying out by parts integral,I get <xp>*= -iħ +<xp> ≠ <xp> .Hence, given expression for <xp> is not real where it should be so. [What I am woried about,even <xp> comes out to be imaginary, <xp>-<px>=iħ is still OK.Because <xp>*=<px>] Also,my attempts to show the second proposed expression leads to imaginary value failed: <xp>=∫ψ* x(ħ/i)(∂/∂x)xψ dx => <xp>*=∫ψ x(-ħ/i) (∂/∂x)xψ* dx =><xp>*=(iħ) ∫ψx (∂/∂x)xψ* dx =(iħ) [-∫xψ*(ψ+ x(∂ψ/∂x)) dx + 0] where I assumed [x²ψ*ψ] gives zero in both +∞ and -∞ limit. [I am not sure at this point too.As the term involves a factor x²] Can anyone suggest if I am going through the correct way?If I am doing wrong in integration, please show it.