相关论文: Relativistic Quantum Newton's Law and photon traje…

Using the relativistic quantum stationary Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding oneself on both relativistic and quantum Lagrangians, we construct a Lagrangian of a relativistic quantum…

Using the quantum Hamilton-Jacobi equation within the framework of the equivalence postulate, we construct a Lagrangian of a quantum system in one dimension and derive a third order equation of motion representing a first integral of the…

For a one-dimensional stationary system, we derive a third order equation of motion representing a first integral of the relativistic quantum Newton's law. We then integrate this equation in the constant potential case and calculate the…

In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a non-relativistic spinless system. This Lagrangian is written as a difference between a function $T$, which represents the…

Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…

It is shown that for a relativistic particle moving in an electromagnetic field its equations of motion written in a form of the second law of Newton can be reduced with the help of elementary operations to the Hamilton-Jacobi equation. The…

One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…

A general formalism for obtaining the Lagrangian and Hamiltonian for a one dimensional dissipative system is developed. The formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The…

In the framework of Lagrangian formulation, some q-deformed physical systems are considered. The q-deformed Legendre transformation is obtained for the free motion of a non-relativistic particle on a quantum line. This is subsequently…

We start with the cosmic Friedmann equations, where we adopt a novel perspective rooted in a Lagrangian formulation grounded in Newtonian mechanics and the first law of thermodynamics. Our investigation operates under the assumption that…

The relativistic equations for the electromagnetic and gravitation interactions are similar: The only Lagrangian equation is the equation with Lorentz force. The potential satisfies the wave equation with the right - hand side proprtional…

We examine the problem of defining Lagrangian and Hamiltonian mechanics for a particle moving on a quantum plane $Q_{q,p}$. For Lagrangian mechanics, we first define a tangent quantum plane $TQ_{q,p}$ spanned by noncommuting particle…

Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion…

In this paper, we introduce a deterministic approach of quantum mechanics for particles with spin 1 2 moving in one dimension. We present a Lagrangian of a spinning particle ($s ={1 \over 2} $), and deduce the expression of the conjugate…

A quantum model based on a Euler-Lagrange variational approach is proposed. In analogy with the classical transport, our approach maintain the description of the particle motion in terms of trajectories in a configuration space. Our method…

Through the constant potential and the linear potential, we establish the existence of nodes for the relativistic quantum trajectories as the same way as for the quantum trajectories. We establish the purely relativistic limit $(\hbar \to…

Free vector fields, satisfying the Lorenz condition, are investigated in details in the momentum picture of motion in Lagrangian quantum field theory. The field equations are equivalently written in terms of creation and annihilation…

Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…

The purpose of this paper is to sketch an approach towards a reconciliation of quantum theory with relativity theory. It will actually be argued that these two theories ultimately rely on one another. A general operator-algebraic framework…

In the present article, we construct a 2D formulation of quantum gravity in the framework of a deterministic theory. In this context, a Quantum stationary Hamilton-Jacobi equation is derived from the Klein- Gordon equation written in the…