相关论文: PT -symmetric harmonic oscillators
The recently proposed PT-symmetric quantum mechanics works with complex potentials which possess, roughly speaking, a symmetric real part and an anti-symmetric imaginary part. We propose and describe a new exactly solvable model of this…
Version 1: The well known Eckart's singular s-wave potential is PT-symmetrically regularized and continued to the whole real line. The new model remains exactly solvable and its bound states remain proportional to Jacobi polynomials. Its…
We describe a novel class of quantum mechanical particle oscillations in both relativistic and non-relativistic systems based on $PT$ symmetry and $T^2=-1$ (relevant for fermions), where $P$ is parity and $T$ is time reversal. The…
A family of spherical non-Hermitian potentials is studied. It is shown that the corresponding non-Hermitian Hamiltonians admit some "new" P$phi$T$phi$-symmetry. It is observed that whilst such P$phi$T$phi$-symmetric Hamiltonians just copy…
In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere PT invariance the superposition V(x) = x^2+ Ze^2/x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze^2=if)…
SUSY partnership between singular potentials often breaks down. Via regularization it can be restored on certain ad hoc subspaces of Hilbert space [Das and Pernice, Nucl. Phys. B 561 (1999) 357]. Within the naturally complexified (so called…
We analyse some PT-symmetric oscillators with $T_{d}$ symmetry that depend on a potential parameter $g$. We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of $g$. Pairs of…
In the recent years a generalization of Hermiticity was investigated using a complex deformation H=p^2 +x^2(ix)^\epsilon of the harmonic oscillator Hamiltonian, where \epsilon is a real parameter. These complex Hamiltonians, possessing PT…
The potential -x^4, which is unbounded below on the real line, can give rise to a well-posed bound state problem when x is taken on a contour in the lower-half complex plane. It is then PT-symmetric rather than Hermitian. Nonetheless it has…
We construct an isospectrum systems in terms of a real and complex potential to show that the underlying PT symmetric Hamiltonian possesses a real spectrum which is shared by its real partner.
The classical trajectories of the family of complex PT-symmetric Hamiltonians $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) form closed orbits. All such complex orbits that have been studied in the past are PT symmetric (left-right symmetric).…
The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of ${\cal PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians…
Large families of Hamiltonians that are non-Hermitian in the conventional sense have been found to have all eigenvalues real, a fact attributed to an unbroken PT symmetry. The corresponding quantum theories possess an unconventional scalar…
For the PT symmetric potential of Dorey, Dunning and Tateo we show that in the large angular momentum (i.e., strongly spiked) limit the low-lying eigenstates of this popular non-Hermitian problem coincide with the shifted Hermitian harmonic…
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…
We notice that PT symmetric non-Hermitian one dimensional simple Harmonic Oscillator under simultaneous transformation of co-ordinate and momentum with proper choice of positive oscillating frequency can reflect negative spectrum with well…
The family of complex PT-symmetric sextic potentials is studied to show that for various cases the system is essentially quasi-solvable and possesses real, discrete energy eigenvalues. For a particular choice of parameters, we find that…
Schroedinger equation H \psi=E \psi with PT - symmetric differential operator H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at a>0. The proof of…
In ${\cal PT}-$symmetric quantum mechanics one of the most characteristic mathematical features of the formalism is the explicit Hamiltonian-dependence of the physical Hilbert space of states ${\cal H}={\cal H}(H)$. Some of the most…
The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian $\cal PT$-symmetric part, is re-examined in the light…