1,721,105 research outputs found
Scattering by PT-Symmetric Non-Local Potentials
No full textA general formalism is worked out for the description of one-dimensional scattering by separable non-local potentials and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the Hamiltonian. The one-dimensional Yamaguchi potential is discussed in detail
Reflectionless PT-Symmetric Potentials in the One-dimensional Dirac Equation
No full textWe study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions, the bound-state spectra are real and the potentials are reflectionless and conserve unitarity in the scattering process. The absence of reflection makes it meaningful to consider also PT-symmetric potentials that do not vanish asymptotically
Overcritical PT-Symmetric Square Well Potential in the Dirac Equation
No full textWe study scattering properties of a PT-symmetric square well potential with real depth larger than the threshold of particle-antiparticle pair production as the time component of a vector potential in the Dirac equation. Spontaneous pair production inside the well becomes tiny beyond the strength at which discrete bound states with real energies disappear, consistently with a spontaneous breakdown of PT symmetry
Non-local PT-Symmetric Potentials in the One-Dimensional Dirac Equation
No full textThe Dirac equation in (1+1) dimensions with a non-local PT-symmetric potential of separable type is studied by means of the Green's function method: properties of bound and scattering states are derived in full detail and numerical results are shown for a potential kernel of Yamaguchi type, inspired by the treatment of low-energy nucleon-nucleon interaction
PT Symmetry Breaking and Explicit Expressions for the Pseudo-Norm in the Scarf II Potential
No full textClosed expressions are derived for the pseudo-norm, norm and orthogonality relations for arbitrary bound states of the PT symmetric and the Hermitian Scarf II potential for the first time. The pseudo-norm is found to have indefinite sign in general. Some aspects of the spontaneous breakdown of PT symmetry are analyzed
Scattering in PT-Symmetric Quantum Mechanics
No full textA general formalism is worked out for the description of one-dimensional scattering in non-her ̈mitian quantum mechanics and constraints on transmission and reflection coefficients ore derived in the cases of P, T or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials ore shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with Hermiticity, T invariance and PT invariance
The Interplay of Different Symmetries in Quantum Mechanical Potentials
No full textWe construct an so (2,2) potential algebra and discuss how it is influenced when PT symmetry is imposed on the potential. We illustrate the procedure with the PT symmetric Scarf II potential
PT-Symmetric Potentials and the so(2,2) Algebra
No full textStarting from a differential realization of the generators of the so(2, 2) algebra we connect the eigenvalue equation of the Casimir invariant either with the hypergeometric equation, or the Schrodinger equation. In the latter case we consider problems for which so(2, 2) appears as a potential algebra, connecting states with the same energy in different potentials. We analyse the role of the two so(2, 1) subalgebras and point out their importance for PT-symmetric problems, where the doubling of bound states is known to occur. We present two mechanisms for this and illustrate them with the example of the Scarf and the Poschl-Teller II potentials. We also analyse scattering states, transmission and reflection coefficients for these potentials
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