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Derivation of the Boltzmann principle
We derive the Boltzmann principle SB=kB ln W based on classical mechanical models of thermodynamics. The argument is based on the heat theorem and can be traced back to the second half of the 19thExpand
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Gauge transformations and the electric dipole approximation
Some subtle aspects of the electric dipole approximation (EDA) are discussed, and some persistent criticisms answered. The usual form of the EDA is that the scalar potential is −E⋅r and the vectorExpand
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Canonical transformation to energy and ‘‘tempus’’ in classical mechanics
In classical Hamiltonian dynamics for a system with a single degree of freedom a canonical transformation is made to new canonical variables in which the new canonical momentum is energy and itsExpand
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Gauge invariant formulation of the interaction of electromagnetic radiation and matter
The conventional perturbation theory in quantum mechanics for the interaction of electromagnetic radiation with matter, which is based on the time‐dependent vector and scalar potentials, is shown toExpand
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Lagrangians for dissipative systems
A Lagrangian and Hamiltonian formulation can be given for a damped harmonic oscillator with damping linear in the velocity. The canonical momentum is not equal to the kinetic momentum, and theExpand
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Helmholtz theorem for antisymmetric second‐rank tensor fields and electromagnetism with magnetic monopoles
A generalized Helmholtz’s theorem is proved, which states that an antisymmetric second‐rank tensor field in 3+1 dimensional space‐time, which vanishes at spatial infinity, is determined by itsExpand
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Generalized Berry phase for the most general time-dependent damped harmonic oscillator
The most general time-dependence Hamiltonian for a harmonic oscillator is both linear and quadratic in the coordinate and the canonical momentum. It describes in general a harmonic oscillator with aExpand
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