We present the quantum mechanics problem of the one-dimensional Schroedinger equation with the trigonometric Rosen-Morse potential. This potential is of possible interest to quark physics in so far as it captures the essentials of the QCD quark-gluon dynamics and (i) interpolates between a Coulomb-like potential (associated with one-gluon exchange) and the infinite wall potential (associated with asymptotic freedom), (ii) reproduces in the intermediary region the linear confinement potential (associated with multi-gluon self-interactions) as established by lattice QCD calculations of hadron properties. Moreover, its exact real solutions given here display a new class of real orthogonal polynomials and thereby interesting mathematical entities in their own.
Relativistic Energy Analysis Of Five Dimensional q-Deformed Radial Rosen-Morse Potential Combined With q-Deformed Trigonometric Scarf Non-Central Potential Using Asymptotic Iteration Method (AIM)
Low-lying spectra in anharmonic three-body oscillators with a strong short-range repulsion
研究了一维三体薛定谔方程。它的两体相互作用被假定由长程吸引力（由L次方势主导）与短程排斥力（由（-K）次方核主导）叠加组成，如果需要，还可以加上次主导幂律分量。在极雅可比坐标系中给出了Calogero模型（在L = K = 2时是可分可解的例外）的不可解不可分推广。我们推导出一组三角恒等式的潜力，推广了众所周知的K=2身份的Calogero的所有整数。这使我们能够以令人惊讶的紧凑形式写出相关的偏微分薛定谔方程。因此，我们能够证明，所有这些模型成为可分离的和可解的强排斥的限制。
Bound states of the Klein-Gordon equation in D-dimensions with some physical scalar and vector exponential-type potentials including orbital centrifugal term
