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Diagonalizable pseudo-Hermitian Hamiltonians with real and discrete spectra, which are superpartners of Hermitian Hamiltonians, must be $eta$-pseudo-Hermitian with Hermitian, positive-definite and non-singular $eta$ operators. We show that despite the fact that an $eta$ operator produced by a supersymmetric transformation, corresponding to the exact supersymmetry, is singular, it can be used to find the eigenfunctions of a Hermitian operator equivalent to the given pseudo-Hermitian Hamiltonian. Once the eigenfunctions of the Hermitian operator are found the operator may be reconstructed with the help of the spectral decomposition.
One of the simplest non-Hermitian Hamiltonians first proposed by Schwartz (1960 {it Commun. Pure Appl. Math.} tb{13} 609) which may possess a spectral singularity is analyzed from the point of view of non-Hermitian generalization of quantum mechanics
We consider the geometrization of quantum mechanics. We then focus on the pull-back of the Fubini-Study metric tensor field from the projective Hibert space to the orbits of the local unitary groups. An inner product on these tensor fields allows us
After recalling different formulations of the definition of supersymmetric quantum mechanics given in the literature, we discuss the relationships between them in order to provide an answer to the question raised in the title.
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the study of sepa
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit, photon-number