Difference between Hamiltonian operator and Total energy operator?

  • Thread starter annms
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  • #1
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What is the difference between the Hamiltonian operator and the Total energy operator? If both is used when working with total energy, why are there two different operators?
 
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  • #2
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They are both sides to the same equation. Hamiltonian = H and total energy = E.
H \psi = E \psi
 
  • #3
SpectraCat
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What is the difference between the Hamiltonian operator and the Total energy operator? If both is used when working with total energy, why are there two different operators?
As far as I am aware, they are one and the same. What was the context that led you to think they might be different?
 
  • #4
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Thank you for the responses guys. Forgive me for asking such a stupid question, I am a newbie to quantum mechanics. I was just reading my textbook and it first listed the total energy operator, then a few pages later it listed the Hamiltonian operator. It just looked very different than the total energy operator to me so I guess I was confused. Thanks again for the responses.
 
  • #5
Bill_K
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In the time-dependent Schrodinger Equation (ih ∂/∂t) ψ = H ψ, people sometimes mistakenly refer to the left hand side ih ∂/∂t as the energy operator. It is not, of course, it merely describes how ψ(x, t) evolves with time. It does not appear in the time-independent Schrodinger equation H ψ = E ψ, and it appears but has a different meaning in other "pictures", e.g. the Heisenberg picture in which (ih ∂/∂t) ψ = 0 and the time evolution is cast onto the operators themselves, or the interaction picture in which (ih ∂/∂t) ψ = Hint ψ where Hint is the interaction Hamiltonian.
 

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