On Domains of PT Symmetric Operators Related to -y''(x) + (-1)^n x^{2n}y(x)
arXiv:0911.1284 · doi:10.1088/1751-8113/43/17/175303
Abstract
In the recent years a generalization of Hermiticity was investigated using a complex deformation H=p^2 +x^2(ix)^εof the harmonic oscillator Hamiltonian, where εis a real parameter. These complex Hamiltonians, possessing PT symmetry (the product of parity and time reversal), can have real spectrum. We will consider the most simple case: εeven. In this paper we describe all self-adjoint (Hermitian) and at the same time PT symmetric operators associated to H=p^2 +x^2(ix)^ε. Surprisingly it turns out that there are a large class of self-adjoint operators associated to H=p^2 +x^2(ix)^εwhich are not PT symmetric.
References in corpus (16)
- Making Sense of Non-Hermitian Hamiltonians
- A non-Hermitian symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
- An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
- Projective Hilbert space structures at exceptional points
- Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
- MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
- Classical Trajectories for Complex Hamiltonians
- Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
- Perturbation theory of PT-symmetric Hamiltonians
- Conditional observability
- Bounds on variation of spectral subspaces under J-self-adjoint perturbations
- symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum
- -self-adjoint operators with -symmetries: extension theory approach
- PT-Symmetric Quantum Theory Defined in a Krein Space
- General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space
- Quantum toboggans with two branch points