科研之友
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摘要
Hamiltonian H that is not Hermitian can still have a real and complete energy eigenspectrum if it instead is PT symmetric. For such Hamiltonians, three possible inner products have been considered in the literature, the V norm, the PT norm, and the C norm. Here, V is the operator that implements VHV-1 = H+, the PT norm is the overlap of a state with its PT conjugate, and C is a discrete linear operator that always exists for any Hamiltonian that can be diagonalized. Here, we show that it is the V norm that is the most fundamental as it is always chosen by the theory itself. In addition, we show that the V norm is always equal to the PT norm if one defines the PT conjugate of a state to contain its intrinsic PT phase. We discuss the conditions under which the V norm coincides with the C operator norm and show that, in general, one should not use the linear C operator, but for the purposes that it is used one can instead use the antilinear PT operator itself.
- 出版日期2018-2-1
