اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدIntegrable conditions for Dirac Equation and Schrodinger equation
216
0
0.0
(
0
)
تأليف
Ying-Qiu Gu
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
By constructing the commutative operators chain, we derive the integrable conditions for solving the eigenfunctions of Dirac equation and Schrodinger equation. These commutative relations correspond to the intrinsic symmetry of the physical system, which are equivalent to the original partial differential equation can be solved by separation of variables. Detailed calculation shows that, only a few cases can be completely solved by separation of variables. In general cases, we have to solve the Dirac equation and Schrodinger equation by effective perturbation or approximation methods, especially in the cases including nonlinear potential or self interactive potentials.
قيم البحث
اقرأ أيضاً
We discuss the structure of the Dirac equation and how the nilpotent and the Majorana operators arise naturally in this context. This provides a link between Kauffmans work on discrete physics, iterants and Majorana Fermions and the work on nilpotent
structures and the Dirac equation of Peter Rowlands. We give an expression in split quaternions for the Majorana Dirac equation in one dimension of time and three dimensions of space. Majorana discovered a version of the Dirac equation that can be expressed entirely over the real numbers. This led him to speculate that the solutions to his version of the Dirac equation would correspond to particles that are their own anti-particles. It is the purpose of this paper to examine the structure of this Majorana-Dirac Equation, and to find basic solutions to it by using the nilpotent technique. We succeed in this aim and describe our results.
In this paper we prove the following: (1) The basic error of time-dependent perturbation theory is using the sum of first finite order of perturbed solutions to substitute the exact solution in the divergent interval of the series for calculating the
transition probability. In addition quantum mechanics neglects the influence of the normality condition in the continuous case. In both cases Fermi golden rule is not a mathematically reasonable deductive inference from the Schrodinger equation. (2) The transition probability per unit time deduced from the exact solution of the Schrodinger equation is zero, which cannot be used to describe the transition processes.
We obtain solutions of the (2 + 1) dimensional k deformed Dirac equation in the presence of crossed magnetic and electric fields. It is shown that the k deformed Landau levels are modified in the presence of the electric field. Contraction of Landau
levels has also been examined and it has been shown that the contraction depends on a critical magnetic field which is independent of the deformation parameter in first order approximation.
The wave equation generalizing the Dirac operator to the Z3-graded case is introduced, whose diagonalization leads to a sixth-order equation. It intertwines not only quark and anti-quark state as well as the u and d quarks, but also the three colors,
and is therefore invariant under the product group Z2 x Z2 x Z3. The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry and of the SU(2) x U(1) that arise automatically in this model, leading to the full bosonic gauge sector of the Standard Model.
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described by the wa
ve function is subatomic particle moving randomly. Therefore, the characteristics of quantum mechanics have a dual nature, one of them is the deterministic nature carried on from classical physics, and the other is the probabilistic nature coined by particles random motion. Based on this model, almost all of open questions in quantum mechanics can be explained consistently, which include the particle-wave duality, the principle of quantum superposition, the interference pattern of double-slit experiments, and the boundary between classical world and quantum world.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
