Consider the operator family H(g):=H_0+igW. H_0 is the quantum harmonic oscillator with rational frequencies , W a P symmetric bounded potential, and g a real coupling constant. We show that if |g|< does not exceed an explicitly determined constant, the spectrum of H(g) is real and discrete. Moreover we show that the ope-rator H(g)=a*_1 a_1+a*_2a_2+ig a*_2a_1 has real discrete spectrum but is not diagonalizable.
PT symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum
CALICETI, EMANUELA;GRAFFI, SANDRO;
2007
Abstract
Consider the operator family H(g):=H_0+igW. H_0 is the quantum harmonic oscillator with rational frequencies , W a P symmetric bounded potential, and g a real coupling constant. We show that if |g|< does not exceed an explicitly determined constant, the spectrum of H(g) is real and discrete. Moreover we show that the ope-rator H(g)=a*_1 a_1+a*_2a_2+ig a*_2a_1 has real discrete spectrum but is not diagonalizable.File in questo prodotto:
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