scholarly journals Absence of a consistent classical equation of motion for a mass-renormalized point charge

2008 ◽  
Vol 78 (4) ◽  
Author(s):  
Arthur D. Yaghjian
Keyword(s):  
Point Charge ◽  
Classical Equation ◽  
Equation Of Motion

Coherent states, Schrödinger equation, and the Hamilton–Jacobi equation

1995 ◽  
Vol 73 (7-8) ◽  
pp. 478-483
Author(s):  
Rachad M. Shoucri
Keyword(s):  
Schrödinger Equation ◽  
Jacobi Equation ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Hidden Variables ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Phase Variable ◽  
Independent Variable ◽  
Hamilton Jacobi Equation

The self-adjoint form of the classical equation of motion of the harmonic oscillator is used to derive a Hamiltonian-like equation and the Schrödinger equation in quantum mechanics. A phase variable ϕ(t) instead of time t is used as an independent variable. It is shown that the Hamilton–Jacobi solution in this case is identical with the solution obtained from the Schrödinger equation without the need to introduce the idea of hidden variables or quantum potential.

A Covariant Semi-Classical Theory of the Radiating Electron

1977 ◽  
Vol 32 (1) ◽  
pp. 101-102
Author(s):  
M. Sorg
Keyword(s):  
Classical Theory ◽  
Characteristic Length ◽  
Order Approximation ◽  
Classical Equation ◽  
Radiation Reaction ◽  
Equation Of Motion ◽  
Compton Wavelength ◽  
Classical Electron ◽  
Electron Radius ◽  
Classical Electron Radius

Abstract A new semi-classical equation of motion is suggested for the radiating electron. The characteristic length of the new theory is the Compton wavelength λc(= ħ/2 m c) instead of the classical electron radius which is used in all purely classical theories of the radiating electron. However, the lowest order approximation of the radiation reaction contains only the classical radius rc.

scholarly journals THE SELF-FORCE OF A CHARGED PARTICLE IN CLASSICAL ELECTRODYNAMICS WITH A CUTOFF

1999 ◽  
Vol 13 (03) ◽  
pp. 315-324 ◽  
Author(s):  
J. FRENKEL ◽  
R. B. SANTOS
Keyword(s):  
Charged Particle ◽  
Special Relativity ◽  
Point Charge ◽  
Equation Of Motion ◽  
The Self ◽  
Classical Electrodynamics ◽  
Exact Equation ◽  
Electromagnetic Mass ◽  
Self Force

We discuss, in the context of classical electrodynamics with a Lorentz invariant cutoff at short distances, the self-force acting on a point charged particle. It follows that the electromagnetic mass of the point charge occurs in the equation of motion in a form consistent with special relativity. We find that the exact equation of motion does not exhibit runaway solutions or non-causal behavior, when the cutoff is larger than half of the classical radius of the electron.

Coherent states and geometric phases of a generalized damped harmonic oscillator with time-dependent mass and frequency

2014 ◽  
Vol 28 (26) ◽  
pp. 1450177 ◽  
Author(s):  
I. A. Pedrosa ◽  
D. A. P. de Lima
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Quantum Invariant ◽  
Dynamical Phase ◽  
Special Cases ◽  
Berry Phases ◽  
Dependent Mass

In this paper, we study the generalized harmonic oscillator with arbitrary time-dependent mass and frequency subjected to a linear velocity-dependent frictional force from classical and quantum points of view. We obtain the solution of the classical equation of motion of this system for some particular cases and derive an equation of motion that describes three different systems. Furthermore, with the help of the quantum invariant method and using quadratic invariants we solve analytically and exactly the time-dependent Schrödinger equation for this system. Afterwards, we construct coherent states for the quantized system and employ them to investigate some of the system's quantum properties such as quantum fluctuations of the coordinate and the momentum as well as the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary system. Finally, we evaluate the dynamical and Berry phases for three special cases and surprisingly find identical expressions for the dynamical phase and the same formulae for the Berry's phase.

QUANTUM BOUNCE OF A UNIFORM DUST STAR IN NEWTON GRAVITY

1991 ◽  
Vol 06 (10) ◽  
pp. 855-859 ◽  
Author(s):  
H. ISHIHARA ◽  
S. MORITA ◽  
H. SATO
Keyword(s):  
Wave Packet ◽  
Numerical Method ◽  
Quantum Dynamics ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Quantum Systems ◽  
Newtonian Limit ◽  
Newtonian Gravity

We investigate the quantum dynamics of a dust sphere collapsing uniformly in Newtonian gravity, in which the concept of time is obvious. The quantum bounce of the wave packet is observed by a numerical method. Our Newton Lagrangian is different from the Newtonian limit of the Einstein Lagrangian. They give the same classical equation of motion but derive the different quantum systems.

Fuzzy Transitions from Quantum to Classical Mechanics and New Phenomena of Mesoscopic Objects

1997 ◽  
Vol 52 (1-2) ◽  
pp. 25-30
Author(s):  
J. P. Hsu
Keyword(s):  
Wave Equation ◽  
Classical Mechanics ◽  
Classical Equation ◽  
Experimental Tests ◽  
Equation Of Motion ◽  
Generalized Equation ◽  
Invariant Equation ◽  
Macroscopic Objects ◽  
New Phenomena ◽  
New Phase

Abstract A new "phase invariant" equation of motion for both microscopic and macroscopic objects is proposed. It reduces to the probabilistic wave equation for small masses and the deterministic classical equation for large masses. The motions of mesoscopic objects and fuzzy transitions between quantum and classical mechanics are discussed on the basis of the generalized equation. Experimental tests of new predictions are discussed.

Quantelung der Zeit und Quantenmechanik

1985 ◽  
Vol 40 (5) ◽  
pp. 456-461
Author(s):  
M. Börner
Keyword(s):  
Initial Conditions ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Expectation Values ◽  
Functional Connection ◽  
Probability Densities ◽  
Necessary Existence ◽  
The Moment ◽  
The Universe

If the universe as a whole can be described as an ordered succession of discrete (Eigen-)states, the parameter of this order, a number t (t ∈ ℤ.) plays the role of a quantizised time. Then a particle (with mass m) as a substructure of the universe no longer follows a classical equation of motion with the moment p and the position x. The functional connection between these two quantities is rather a distribution. Especially there no longer exists the classical union of differential equation-initial conditions-path. The path is now only understandable as average, introducing a continuously running time. A central part for finding p̄ and x̄ as such averages, is played by the expectation values of these new quantities. Since the expectation values depend on all discrete points x(t) ( − ∞ ≦ t ≦ + ∞), we find sumrelations, which we can approximate by integrals. The integration extends over all d.x resp. dp-elements, which are loaded with the probability of their appearance. Following this procedure p and x become operators. If we postulate p̄ and p̄ to fulfil Newtons law, we find the ψxand ψp functions, constituting the resp. probability densities, to be governed by Shroedingers equation. The necessary existence of a quantum mechanics can thus be a reference to the existence of a noncontinuous time.

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