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Deriving the Hamiltonian for
Charged Particle in Electro-magnetic Field

We need to have this nicely re-written with sufficient detail, but without too much of it.
In LaTeX ...   But this is good enough for study ....

Bransden and Joachain, Atomic and Moleular Physics, Appendix

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They say: It is then easily shown ....  Well it is not that easy, see below

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This is the final result which we need.
But how about  ... it is easily shown .....

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Goldstein, Classical Mechanics,
Applications of Lagrange Formalism, pages about 20-22

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   Here it starts
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As you see above, it is this adding and subtracting of terms
This is the "easily shown bit"

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The rest is an interesting reading, but (1-65) is just the confirmation of the above result

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