Please stop propagating the misunderstanding that the…
0 reactions
Please stop propagating the misunderstanding that the Dirac equation somehow "replace" the Schrodinger equation
The Schrodinger equation is
iℏ ∂Ψ/∂t = ĤΨ.
The equation iℏ ∂Ψ/∂t = −(ℏ²/2m)∇²Ψ + VΨ is just a special case corresponding to the Hamiltonian of a non-relativistic particle moving in an external potential (expressed in the position basis). By conflating the two and referring to the second as "the" Schrodinger equation, it can confuse people who go onto study relativistic QM and QFT, because they can mistakenly believe iℏ ∂Ψ/∂t = ĤΨ is somehow obsolete, when in reality it follows us through to the deepest parts of quantum theory by telling us that energy is the generator of time translations.
Indeed, the Diraq equation just follows from plugging in the Dirac Hamiltonian,
Ĥ = c α·p + βmc²
into the S.E.
From that pops out
iℏ ∂Ψ/∂t = (−iℏc α·∇ + βmc²)Ψ
and
(iℏγ^(μ) ∂\_μ − mc)ψ = 0.
It drives me nuts to hear educators and students claiming that the Dirac equation somehow replaces or corrects the Schrodinger equation, as though this is another instance of learning a white-lie model (like the Bohr model or Newtonian gravity) and replacing it. I find this can confuse students who continue to study QFT when they learn scattering and the S.E. pops up again. "Wait, isn't that old news?" In reality, the Schrodinger equation was there all along.
#science
The Schrodinger equation is
iℏ ∂Ψ/∂t = ĤΨ.
The equation iℏ ∂Ψ/∂t = −(ℏ²/2m)∇²Ψ + VΨ is just a special case corresponding to the Hamiltonian of a non-relativistic particle moving in an external potential (expressed in the position basis). By conflating the two and referring to the second as "the" Schrodinger equation, it can confuse people who go onto study relativistic QM and QFT, because they can mistakenly believe iℏ ∂Ψ/∂t = ĤΨ is somehow obsolete, when in reality it follows us through to the deepest parts of quantum theory by telling us that energy is the generator of time translations.
Indeed, the Diraq equation just follows from plugging in the Dirac Hamiltonian,
Ĥ = c α·p + βmc²
into the S.E.
From that pops out
iℏ ∂Ψ/∂t = (−iℏc α·∇ + βmc²)Ψ
and
(iℏγ^(μ) ∂\_μ − mc)ψ = 0.
It drives me nuts to hear educators and students claiming that the Dirac equation somehow replaces or corrects the Schrodinger equation, as though this is another instance of learning a white-lie model (like the Bohr model or Newtonian gravity) and replacing it. I find this can confuse students who continue to study QFT when they learn scattering and the S.E. pops up again. "Wait, isn't that old news?" In reality, the Schrodinger equation was there all along.
#science
| 1,000 mlx | |
| 2 | |
| 0 |