phy-4600/notes/particle operators
2016-03-13 20:07:19 -04:00

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Ĥ = T̂ + V̂
with
V̂ = V = V(𝐫,t) (potential energy operator)
and
T̂ = _͟𝐩̂͟⋅͟𝐩̂͟ = _͟p̂͟²͟ = -_͟ħ͟²͟ ∇²
2m 2m 2m
since
p̂ = -ιħ∇.
Ĥ = T̂ + V̂ = -_͟ħ͟²͟ ∇² + V(𝐫,t).
2m