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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?