The idea for this series of videos came from a discussion in my group regarding the "parity switch" related to Bogoliubov-de Gennes (BdG) level crossings mentioned in the "Topology in condensed matter" site:
[ Ссылка ]

In the first video, we starting with a simple quadratic Hamiltonian with superconducting pairing, we show how to obtain the BdG form.

ERRATUM: as pointed out in the comments, the matrix form of the Hamiltonian should be the transposed of what is shown in the video (or you can replace \Delta with \Delta^*). Since we will take Delta to be real later, this does not affect the overall conclusions.

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