I'm a bit puzzled over the structure of the Hamiltonian in the Schrodinger equation (SE). First we take the famous expression, Eψ=Hψ. From what I'm aware of, the classical Hamiltonian is H=Kinetic energy (KE) + Potential energy (PE). However, in the SE, there appears to be a negative sign before the KE term in the rhs representing the Hamiltonian, i.e., E = -KE + PE, which would seem to imply that H=PE-KE. Can someone help reconcile this apparent discrepancy for me?