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It is shown that if the C operator for a PT-symmetric Hamiltonian with simple eigenvalues is not unique, then it is unbounded. Apart from the special cases of finite-matrix Hamiltonians and Hamiltonians generated by differential expressions with PT-symmetric point interactions, the usual situation is that the C operator is unbounded. The fact that the C operator is unbounded is significant because, while there is a formal equivalence between a PT-symmetric Hamiltonian and a conventionally Hermitian Hamiltonian in the sense that the two Hamiltonians are isospectral, the Hilbert spaces are inequivalent. This is so because the mapping from one Hilbert space to the other is unbounded. This shows that PT-symmetric quantum theories are mathematically distinct from conventional Hermitian quantum theories.
We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, i
We have briefly analyzed the existence of the pseudofermionic structure of multilevel pseudo-Hermitian systems with odd time-reversal and higher order involutive symmetries. We have shown that 2N-level Hamiltonians with N-order eigenvalue degeneracy
A cornerstone of quantum mechanics is the characterisation of symmetries provided by Wigners theorem. Wigners theorem establishes that every symmetry of the quantum state space must be either a unitary transformation, or an antiunitary transformation
We consider the Schr{o}dinger equation with a nondispersive logarithmic nonlinearity and a repulsive harmonic potential. For a suitable range of the coefficients, there exist two positive stationary solutions, each one generating a continuous family
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position-dependent mas