Minimal length curves in unitary orbits of a Hermitian compact operator

Minimal length in Quantum Mechanics and non-Hermitian Hamiltonian systems

Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator

The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the existence of a positivedefinite inner product that renders the Hamiltonian self-adjoint. Unlike for a time-independent Hamiltonian, this does not imply the uni...

Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty

We study non-Hermitian quantummechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in both the cases are found to be real. It is also shown that the models are η pseudo-Hermitian and the metric operator is found explicitly in both the cases.

Comment on “Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty”

We demonstrate that the recent paper by Jana and Roy entitled “Non-Hermitian quantum mechanics with minimal length uncertainty” [SIGMA 5 (2009), 083, 7 pages, arXiv:0908.1755] contains various misconceptions. We compare with an analysis on the same topic carried out previously in our manuscript [arXiv:0907.5354]. In particular, we show that the metric operators computed for the deformed non-Her...

On local CR-transformations of Levi-degenerate group orbits in compact Hermitian symmetric spaces

We present a large class of homogeneous 2-nondegenerate CR-manifolds M , both of hypersurface type and of arbitrarily high CR-codimension, with the following property: Every CRequivalence between domains U,V inM extends to a global real-analytic CR-automorphism ofM . We show that this class containsG-orbits in Hermitian symmetric spaces Z of compact type, where G is a real form of the complex L...