ترغب بنشر مسار تعليمي؟ اضغط هنا

Quantum Dynamical Algebra SU(1,1) in One-Dimensional Exactly Solvable Potentials

60   0   0.0 ( 0 )
 نشر من قبل MingGuang Hu
 تاريخ النشر 2007
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We mainly explore the linear algebraic structure like SU(2) or SU(1,1) of the shift operators for some one-dimensional exactly solvable potentials in this paper. During such process, a set of method based on original diagonalizing technique is presented to construct those suitable operator elements, J0, J_pm that satisfy SU(2) or SU(1,1) algebra. At last, the similarity between radial problem and one-dimensional potentials encourages us to deal with the radial problem in the same way.

قيم البحث

اقرأ أيضاً

In a previous paper [{it J. Phys. A: Math. Theor.} {bf 40} (2007) 11105], we constructed a class of coherent states for a polynomially deformed $su(2)$ algebra. In this paper, we first prepare the discrete representations of the nonlinearly deformed $su(1,1)$ algebra. Then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su(1,1) algebra which contains the Barut-Girardello set and the Perelomov set of the SU(1,1) coherent states as special cases. We also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem.
A protocol for explicitly constructing the exact time-evolution operators generated by $2 times 2$ time-dependent $PT$-symmetry Hamiltonians is reported. Its mathematical applicability is illustrated with the help of appropriate examples. The physica l relevance of the proposed approach within gain-loss system scenarios, like two-coupled wave-guides, is discussed in detail.
65 - A. Lopez-Ortega 2016
Based on a method that produces the solutions to the Schrodinger equations of partner potentials, we give two conditionally exactly solvable partner potentials of exponential type defined on the half line. These potentials are multiplicative shape in variant and each of their linearly independent solution includes a sum of two hypergeometric functions. Furthermore we calculate the scattering amplitudes and study some of their properties.
84 - A. Lopez-Ortega 2015
We give two conditionally exactly solvable inverse power law potentials whose linearly independent solutions include a sum of two confluent hypergeometric functions. We notice that they are partner potentials and multiplicative shape invariant. The m ethod used to find the solutions works with the two Schrodinger equations of the partner potentials. Furthermore we study some of the properties of these potentials.
It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin-1/2 spin-1 ladder, a mixed spin-1/2 spin-3/2 ladder and a spin-1 ladder with biquadratic interactions.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا