ABSTRACT
We look for a Hamiltonian to use in the time-dependent Schrödinger equation, and because this is first order in time we stay first order in space trying to treat all coordinates on a similar basis. Write https://www.w3.org/1998/Math/MathML"> i ∂ ψ ∂ t = H ψ = − i α i ∂ ψ ∂ x i + m β ψ i = 1 , 2 , 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429184550/c5a9cf84-23e1-4064-9971-05f6815a4e54/content/math4_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where ψ is now a column and the αi and β are square matrices.
