ABSTRACT
To obtain a Lorentz invariant Schrödinger equation, we considered the square root of the Klein–Gordon equation. This had the disadvantage that the Hamiltonian https://www.w3.org/1998/Math/MathML"> H = p → 2 + m 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429073601/03ca065d-1bf0-4218-811d-2f95276252a3/content/equ_603.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> contains an infinite number of powers of https://www.w3.org/1998/Math/MathML"> p → 2 / m 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429073601/03ca065d-1bf0-4218-811d-2f95276252a3/content/equ_604.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , the parameter in which the square root should be expanded. It would have been better to treat space and time on a more equal footing in the Schrödinger equation. This is what Dirac took as his starting point. As the Schrödinger equation is linear in https://www.w3.org/1998/Math/MathML"> p 0 = i ∂ / ∂ t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429073601/03ca065d-1bf0-4218-811d-2f95276252a3/content/equ_605.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , one is looking for a Hamiltonian that is linear in the momenta https://www.w3.org/1998/Math/MathML"> p j = i ∂ / ∂ x j ( = − p j ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429073601/03ca065d-1bf0-4218-811d-2f95276252a3/content/equ_606.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ). () https://www.w3.org/1998/Math/MathML"> i ∂ Ψ ∂ t = H Ψ = − i α k ∂ Ψ ∂ x k + β m Ψ . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429073601/03ca065d-1bf0-4218-811d-2f95276252a3/content/equ_607.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
