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.
E.Caliceti, S.Graffi, J.Sjoestrand (2007). PT symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 40, 10155-10170 [10.1088/1751-8113/40/33/014].
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
