Passage from the BHJ paper, in German, showing the decomposition of the field into Fourier modes with time-dependent coefficients. The Hamiltonian is then written in terms of these modes.

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1. Robert McNees (mcnees@mastodon.social)'s status on Friday, 02-Feb-2024 15:17:20 UTC Robert McNees

   in reply to

   BHJ considered a field that depends on time and a single spatial direction x which runs from 0 < x < L. The field is set to zero at the ends, just like the boundary conditions you would use for the displacement of a string on a guitar or violin.

   They expanded the field in Fourier modes, wrote the time-dependent coefficients of the modes as creation and annihilation operators, and imposed the usual commutation relations.

   It was like they were quantizing the excitations of a string.