Quantum Newton’s Law
نویسنده
چکیده
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 quantum Newton’s law. We then integrate this equation in the free particle case and compare our results to those of Floydian trajectories. Finally, we propose a quantum version of Jacobi’s theorem. PACS: 03.65.Bz; 03.65.Ca
منابع مشابه
Are discrete models more accurate?
Newton’s second law describes the motion of the center of mass of most objects that we encounter in everyday life, including the complex motion of a spoon when we eat, the acceleration of a car, and even the trajectories of planets and stars. Only if objects move extremely fast, do we need to replace Newton’s second law with Einstein’s theory of relativity, and only if objects are extremely sma...
متن کاملIntroducing the notion of bare and effective mass via Newton’s second law of motion
The concepts of bare and effective mass are widely used within modern physics. Their meaning is discussed in advanced undergraduate and graduate courses such as solid state physics, nuclear physics and quantum field theory. Here I discuss how these concepts may be introduced together with the discussion of Newton’s second law of motion. The setting up of simple equations for the effective mass ...
متن کاملCalculation of the Deflection of Light Ray near the Sun with Quantum-corrected Newton’s Gravitation Law
The deflection of light ray passing near the Sun is calculated with quantum-corrected Newton’s gravitation law. The satisfactory result suggests that there may exist other theoretical possibilities besides the theory of relativity. The deflection of light ray near the Sun was a successful prediction of Einstein’s theory of relativity, to which classical mechanics is futile. That was one of the ...
متن کاملFrom a Mechanical Lagrangian to the Schrödinger Equation. A Modified Version of the Quantum Newton’s Law
In the one-dimensional stationary case, we construct the most general Lagrangian depending on the coordinate x and the temporal derivatives ẋ, ẍ and ̇̈ x, and from which we reproduce the well-known quantum stationary Hamilton-Jacobi equation for a non-relativistic spinless system. Our construction is based on the dimensional analysis and allows us to express the Hamiltonian and then to deduce th...
متن کاملTime-Reversal Invariance and the Relation between Wave Chaos and Classical Chaos
Many imaging techniques depend on the fact that the waves used for imaging are invariant for time reversal. The physical reason for this is that in imaging one propagates the recorded waves backward in time to the place and time when the waves interacted with the medium. In this chapter, the invariance for time reversal is shown for Newton’s law, Maxwell’s equations, the Schrödinger equation an...
متن کامل