From what I understand the Dirac equation is supposed to be an improvement on the Schrödinger equation in that it is consistent with relativity theory. Yet all methods I have encountered for doing actual ab initio quantum mechanical calculations uses the Schrödinger equation. If relativistic effects are important one adds a relativistic correction. If the Dirac equation is a more correct description of reality, shouldn't it give rise to easier calculations? If it doesn't, is it really a more correct description?
Answer
Think it with an example, Einstein's field equations are much more precise than Newton's law of gravity, but it's much more complicated to solve a Classical Mechanics problem with General Relativity.
More fundamental and precise doesn't mean that it will give easier calculations. If it did, then then chemistry, medicine, etc... wouldn't exist because they can be described almost completely using Dirac's equation.
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