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Publication Metadata only Comment on the possibility of a geometric constraint in the Schrodinger quantum mechanics(World Scientific Publ Co Pte Ltd, 2000) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231It is shown that the geometric constraint advocated in [R. S. Kaushal, Mod. Phys. Lett.A15, 1391 (2000)] is trivially satisfied. Therefore, such a constraint does not exist. We also point out another flaw in Kaushal's paper.Publication Metadata only Hilbert space structures on the solution space of Klein-Gordon-type evolution equations(Iop Publishing Ltd, 2003) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We use the theory of pseudo-Hermitian operators to address the problem of the construction and classification of positive-definite invariant inner-products on the space of solutions of a Klein-Gordon-type evolution equation. This involves dealing with the peculiarities of formulating a unitary quantum dynamics in a Hilbert space with a time-dependent inner product. We apply our general results to obtain possible Hilbert space structures on the solution space of the equation of motion for a classical simple harmonic oscillator, a free Klein-Gordon equation and the Wheeler-DeWitt equation for the FRW-massive-real-scalar-field models.Publication Metadata only On the pseudo-hermiticity of a class of PT-symmetric Hamiltonians in one dimension(World Scientific Publ Co Pte Ltd, 2002) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231For a given standard Hamiltonian H = [p - A(x)]2/(2m) + V(x) with arbitrary complex scalar potential V and vector potential A, with x ∈ ℝ, we construct an invertible antilinear operator τ such that H is τ-anti-pseudo-hermitian, i.e. H† = τHτ-1. We use this result to give the explicit form of a linear hermitian invertible operator with respect to which any standard PT-symmetric Hamiltonian with a real degree of freedom is pseudo-hermitian. Our results do not make use of the assumption that H is diagonalizable or that its spectrum is discrete.Publication Metadata only On the statistical origin of topological symmetries(World Scientific Publ Co Pte Ltd, 2002) Samani, Keivan Aghababaei; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We investigate a quantum system possessing a parasupersymmetry of order 2, an orthosupersymmetry of order p, a fractional supersymmetry of order p + 1, and topological symmetries of type (1, p) and (1, 1). We obtain the corresponding symmetry generators, explore their relationship, and show that they may be expressed in terms of the creation and annihilation operators for an ordinary boson and orthofermions of order p. We give a realization of parafermions of order 2 using orthofermions of arbitrary order p, discuss a p = 2 parasupersymmetry between p = 2 parafermions and parabosons of arbitrary order, and show that every orthosupersymmetric system possesses topological symmetries. We also reveal a correspondence between the orthosupersymmetry of order p and the fractional supersymmetry of order p + 1.Publication Metadata only Topological symmetries(World Scientific Publ Co Pte Ltd, 2000) Samani, Keivan Aghababaei; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z(2)-graded uniform topological symmetries of types (1, 1) and (2, 1). This leads to a novel derivation of the algebras of supersymmetry and p = 2 parasupersymmetry.