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Semiconductor Physics, Quantum Electronics & Optoelectronics. 2010. V. 13, N 4. P. 366-368.
Splitting the eigenvectors space for Kildal’s Hamiltonian
1Petro Mohyla Black Sea State University, Department of Medical Devices and Systems,
10, 68 Desantnikov str., 54003 Mykolaiv, Ukraine; e-mail: gp47@mail.ru
Abstract. The rational canonical form of Kildal’s Hamiltonian has been obtained as a
matrix with two identical diagonal blocks. It allowed to formulate and strictly prove few
common assertions. Each of the eigenvalues of Kildal’s Hamiltonian is twice
degenerated everywhere, and it is well-known Kramers’ degeneration, firstly. However,
there is neither degeneration with except for Kramers’, secondly. The symmetry of
Kildal’s Hamiltonian forcedly includes the operation of inversion (i.e. the center of
symmetry), thirdly. Consequently this form of Hamiltonian is evidently not able to
describe the specific properties of crystals without the center of symmetry. The
Frobenius form (alias “the rational canonical form”) of Hamiltonian should consist of
two non-identical diagonal blocks to remove Kramers’ degeneration.
Keywords: Kildal’s Hamiltonian, Kramers’ degeneration, splitting the space of
eigenvectors, rational canonical form.
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