Physics – Quantum Physics
Scientific paper
2008-04-12
Physics
Quantum Physics
10 pages
Scientific paper
We introduce a new class of non-Hermitian Hamiltonians which possesses both $\mathcal{PT}$-symmetric and non-$\mathcal{PT}$-symmetric members. We calculated the corresponding class of positive definite metric operators in a closed form. We showed that the energy spectrum for each member in the class is positive ($E_{n}\geq0)$. To check the physical acceptability of a Hamiltonian in the class, we obtained the ground state functions for each member in a closed form to test their square integrability and conclude that only $\mathcal{PT}$-symmetric members out of the class can have ground state functions belong to the Hilbert space $L^{2}(\mathbb{R}) $. Since the Hamiltonians introduced have an interaction term of the form of a pure function of the position operator times the momentum operator, we reintroduced a closely related class of Hamiltonians for which the ordering ambiguity does not exist. As the metric operators are quasi-gauge transformations and the class introduced has a potential term due to an imaginary magnetic field, they shift the action by a terminal term which will add nothing to the amount of any Physical quantity when calculated in the path integral formulation of the problem.
No associations
LandOfFree
A new class of Pseudo-Hermitian Hamiltonians with Real Positive Spectra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A new class of Pseudo-Hermitian Hamiltonians with Real Positive Spectra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A new class of Pseudo-Hermitian Hamiltonians with Real Positive Spectra will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-474510