QMGreensite_merged

16 CHAPTER1. THECLASSICALSTATE

5. TheHamiltonian

H[{qi,pi}]≡

∑

n

pnq ̇n−L[{qi,q ̇i}] (1.40)

UsuallytheHamiltonianhastheform

H[p,q]=KineticEnergy+PotentialEnergy (1.41)

Finally,theequationsofmotionin1st-orderformaregivenby

6. Hamilton’sEquations

q ̇i =

∂H

∂pi

p ̇i = −

∂H

∂qi

(1.42)