Calculation of C Operator in PT -Symmetric Quantum Mechanics
نویسنده
چکیده
If a HamiltonianH has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT . The inner product with respect to CPT is associated with a positive norm and the quantum theory built on the associated Hilbert space is unitary. In this paper it is shown how to construct the operator C for the non-Hermitian PT -symmetric Hamiltonian H = 12p + 1 2x 2 + i x using perturbative techniques. It is also shown how to construct the operator C for H = 12p 2 + 12x 2 − x using nonperturbative methods [1].
منابع مشابه
Comment on “PT-Symmetric versus Hermitian Formulations of Quantum Mechanics”
We explain why the main conclusion of Bender et al, J. Phys. A 39, 1657 (2006), regarding the practical superiority of the non-Hermitian description of PT -symmetric quantum systems over their Hermitian description is not valid. Recalling the essential role played by the Hermitian description in the characterization and interpretation of the physical observables, we maintain that as far as the ...
متن کامل-Symmetric Cubic Anharmonic Oscillator as a Physical Model
We perform a perturbative calculation of the physical observables, in particular pseudoHermitian position and momentum operators, the equivalent Hermitian Hamiltonian operator, and the classical Hamiltonian for the PT -symmetric cubic anharmonic oscillator, H = 1 2mp 2+ 1 2μ 2x2+iǫx3. Ignoring terms of order ǫ4 and higher, we show that this system describes an ordinary quartic anharmonic oscill...
متن کاملThe C operator in PT -symmetric quantum field theory transforms as a Lorentz scalar
1550-7998=20 A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator called C. It is shown here that C is the complex extension of the intrinsic parity operator and that the C operator transforms under the Lorent...
متن کاملQuantum Squeezed Light Propagation in an Optical Parity-Time (PT)-Symmetric Structure
We investigate the medium effect of a parity-time (PT)-symmetric bilayer on the quantum optical properties of an incident squeezed light at zero temperature (T=0 K). To do so, we use the canonical quantization approach and describe the amplification and dissipation properties of the constituent layers of the bilayer structure by Lorentz model to analyze the quadrature squeezing of the outgoing ...
متن کاملNumerical Analysis of Stability for Temporal Bright Solitons in a PT-Symmetric NLDC
PT-Symmetry is one of the interesting topics in quantum mechanics and optics. One of the demonstration of PT-Symmetric effects in optics is appeared in the nonlinear directional coupler (NLDC). In the paper we numerically investigate the stability of temporal bright solitons propagate in a PT-Symmetric NLDC by considering gain in bar and loss in cross. By using the analytical solutions of pertu...
متن کامل