Some comments on bound state eigenvalues of PT - symmetric potentials
نویسندگان
چکیده
Using purely physical arguments, it is claimed that for ID Schrödinger operators with complex PT-symmetric potentials having a purely real, attractive potential well and a purely imaginary repulsive part, bound state eigenvalues will be discrete and real. This has been illustrated with several potentials possessing similar properties.
منابع مشابه
Bound-States of the Spinless Salpeter Equation for the PT -Symmetric Generalized Hulthén Potential by the Nikiforov-Uvarov Method
The one-dimensional spinless Salpeter equation has been solved for the PT -symmetric generalized Hulthén potential. The Nikiforov-Uvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive an...
متن کاملPT-symmetric Solutions of Schrödinger Equation with position-dependent mass via Point Canonical Transformation
PT-symmetric solutions of Schrödinger equation are obtained for the Scarf and generalized harmonic oscillator potentials with the position-dependent mass. A general point canonical transformation is applied by using a free parameter. Three different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials ar...
متن کاملExact Solution of the Klein-Gordon Equation for the PT -Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method
The one-dimensional Klein-Gordon (KG) equation has been solved for the PT -symmetric generalized Woods-Saxon (WS) potential. The NikiforovUvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have also investigated th...
متن کاملPt-symmetric Non-polynomial Oscillators and Hyperbolic Potential with Two Known Real Eigenvalues in a Susy Framework
Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasiexactly solvable PT-symmetric potentials with two known real eigenvalues (the ground state and first-excited state energies). We construct examples, namely those of complexified non-polynomial oscillators and of a complexified hyperbolic po...
متن کاملScattering in the PT -symmetric Coulomb potential
Scattering on the PT -symmetric Coulomb potential is studied along a Ushaped trajectory circumventing the origin in the complex x plane from below. This trajectory reflects PT symmetry, sets the appropriate boundary conditions for bound states and also allows the restoration of the correct sign of the energy eigenvalues. Scattering states are composed from the two linearly independent solutions...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001