Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials

The scattering states in one-dimensional Hermitian and non-Hermitian potentials are investigated. An analytical solution for the scattering states is presented in terms of Heun functions. It is shown that for some specially chosen parameter conditions, an infinite number of the exact scattering states is obtained. In the Hermitian potentials, they correspond to the reflectionless states. In the non-Hermitian complex potentials with parity-time symmetry, they are the unidirectionally reflectionless states.

Approximate Analytical Solutions for Scattering States of D-dimensional Hulthen Potentials

Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.

The scattering states of the generalized Hulthén potential with an improved new approximate scheme for the centrifugal term

This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the 1-wave SchrSdinger equation for the generalized Hulthen potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthen potential and Woods-Saxon potential are also studied briefly.

Relativistic Scattering States of Coulomb Potential Plus a New Ring-Shaped Potential

In this paper, exact solutions of scattering states of the Klein-Gordon equation with Coulomb potential plus a new ring-shaped potential are studied under the condition that the scalar potential is equal to the vector potential. The normalized wave functions of scattering states on the “k/27π scale” and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed.

Scattering states of modified PSschl-Teller potential in D-dimension

We present a new approximation scheme for the centrifugal term, and apply this new approach to the SchrSdinger equation with the modified P5schl Teller potential in the -dimension for arbitrary angular momentum states. The approximate analytical solutions of the scattering states are derived. The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the 2 scale and the calculation formula of the phase shifts are given. The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method （APM）.

Scattering states of modified Pschl-Teller potential in D-dimension

We present a new approximation scheme for the centrifugal term,and apply this new approach to the Schrdinger equation with the modified Pschl-Teller potential in the D-dimension for arbitrary angular momentum states.The approximate analytical solutions of the scattering states are derived.The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the k/2π scale and the calculation formula of the phase shifts are given.The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method(APM).

Scattering States of l-Wave Schr¨odinger Equation with Modified Rosen–Morse Potential

Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.

Relativistic particle scattering states with tensor potential and spatially-dependent mass

We investigate the relativistic equation for particles with spin 1/2 in the q-parameter modified P5schl- Teller potential, including Coulomb-like tensor interaction with spatially-dependent mass for the D-dimension. We present approximate solutions of the Dirac equation with these potentials for any spin-orbit quantum number k under spin symmetry. The normalized wave functions are expressed in terms of the hyper-geometric series of the scattering states on the k/2π scale. We also give the formula for the phase shifts, and use the Nikiforov-Uvarov method to obtain the energy eigen-values equation.

Scattering Resonance States and Partial Potential Energy Surface of Reaction I+HI(v=0)→IH(v′=0) +I

The partial potential energy surface of the I ＋ HI →IH ＋ I reaction involving the translational and vibrational motions has been constructed at the QCISD（ T ）//MP4SDQ level with the pseudo potential method that is helpful to interpreting the scattering resonance states. The lifetimes of the scattering resonance states in the title reaction obtained from the partial potential energy surface are about 90-120 fs, which agrees with the result of high-resolved threshold photodetachment spectroscopy of anion IHI^- measured by Neumark.

Theoretical Research on Scattering Resonance States of Reaction I＋HI（v=O）→IH（v＇=0）＋I： Partial Potential Energy Surface and One-dimensional Quantum Reactive Scattering Calculation

Based on the vibrational potential curves coupled with the minimum energy reaction path, the partial potential energy surface of the reaction I＋HI→IH＋I was constructed at the QCISD（T）//MP4SDQ level with pseudo potential method. And the formation mechanism of the scattering resonance states of this reaction was well interpreted with the partial potential energy surface. The scattering resonance states of this reaction should belong to Feshbach resonance because of the coupling of the vibrational mode and the translational mode. With the one-dimensional square potential well model, the resonance width and lifetime of the I＋HI（v=0）→IH（v＇=0）＋I state-to-state reaction were calculated, which preferably explained the high-resolved threshold photodetachment spectroscopy of the IHI- anion performed by Neumark et al..

Theoretical Studies on Formation Mechanism of Resonance States for Na+I_2→Na^++I_2^-System

An extended linear combination of arrangement channels-scattering wave-function(LCAC-SW) quantum scattering dynamic method combined with ab initio quantum chemical calculation was used to study the formation mechanism of the resonance states for the collinear Na+I 2→Na ++I - 2 ion-pair formation process on Aten-Lanting-Los potential energy surface. The resonance energy and the resonance width or the lifetime for the first resonance peak were calculated. The resonance can be identified as the Feshbach type and the physical interpretation is given. The geometric structure of the resonance state for the title system has been optimized.

Theoretical Study of the Scattering Resonance State, Reaction Mechanism and Partial Potential Energy Surface of the F+CH4→HF+CH3 Reaction

The partial potential energy surface was constructed by ab initio method [QCISD（T）/6- 311＋＋G（2df,2pd）]for F＋CH4→HF＋CH3 reaction system. It not only explained the reaction mechanism brought forward by Diego Troya by means of quasiclassical trajectory （QCT） but also successfully validated Kopin Liu＇s experimental phenomena about the existence of the reactive resonance. The lifetime of the scattering resonance state was about 0.07 ps. All these were in agreement with the experiments.

Scattering and Bound States of the Dirac Particle for q-Parameter Hyperbolic Pschl-Teller Potential

The one-dimensional Dirac particle for equal scalar and vector asymmetric q-parameter hyperbolic PschlTeller potential (qHPT) is solved in terms of hypergeometric functions. The scattering and bound states are obtained by using the properties of the equation of continuity of the wave functions. We calculat in details the transmission and reflection coefficients.

Theory of ghost scattering with biphoton states

We show how quantum entangled biphoton states can be used to realize ghost scattering, a nonlocal scheme to obtain scattering information of an unknown object through the correlation measurement of the scattering photons in two different optical paths. We present a framework to describe the biphoton ghost scattering process from the T-matrix formula of the scattering theory. We find the scattering information of a test object can be retrieved from either the test arm or the reference arm. By adjusting the biphoton states, the ghost scattering patterns may be varied from the scattering pattern of the object in the test arm to the object in the reference arm.

Relativistic Bound and Scattering Amplitude of Spinless Particles in Modified Schioberg Plus Manning–Rosen Potentials

By using an approximation for the centrifugal term, we study relativistic bound and scattering states of spin-zero particles in the presence of equal scalar and vector modified Schioberg plus Manning–Rosen potentials for any quantum numbers n and l. Energy eigenvalues and the scattering amplitude are calculated. Some special cases of the problem are also investigated.

An Ab initio Theoretical Study on the Nonadiabatic Coupling for Na+I_2 Collision System

The ionic and neutral state potential energy surfaces (PESs) of Na+I 2 collision system have been calculated on QCISD(T) level by using ab initio method. The location and depth of the potential well, the collision radius and their fine structures have been analyzed at the equilibrium geometry of I 2 molecule. The electronic transfer probabilities are also calculated in terms of Landau Zener model. The lifetime of scattering resonance state is evaluated by the uncertainty principle. All the results have been compared with those obtained according to the Aten Lanting Los PES and Feng's PES.