By Laurent Schwartz
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Extra resources for Application of distributions to the theory of elementary particles in quantum mechanics
Galileo's principle is the following: The fundamental laws of mechanics are equally in form in arbitrary reference frames related through the Galilean transformations. In the sys- Figure -2. In the inertial reference frames K and K', the radius-vectors, velocities and times of the particle P are related through the Galileo's transformations and the fundamental laws have the same form. 18) and in the system K' we will denote it as L ′ = L ′ ( v′2 ) . According to Galileo's principle, L ′ = L (v′2 ) , and according to the properties of the Lagrangian function, L ' can differ from the L by the total time derivative of any function of the co-ordinates r and the time t.
2. Why the law of conservation of energy, which has been proved for a closed system, is true also in an external constant potential field? 3. In which cases is the law of momentum conservation valid in an open system? 4. In what reference frame is the momentum of a mechanical system equal to zero? 5. Suppose that two atoms with equal masses and equal but reversed velocities, are collided. Will the velocities of the atoms remain equal after the collision, if: a) before and after the collision the atoms are excited; b) as a result of the collision one or both atoms are excited; c) before the collision one or both atoms were excited?
And the mechanical moment has only a component along the rotational axis. According to the previous paragraph, the conservative component in a field with axial symmetry along the Z-axis is Lz , the beginning of the co-ordinate system can be any point on the Z-axis. Finally, we can summarize the results: originating from the basic properties of time (homogeneity) and space (homogeneity and isotropy), we obtained seven constants of motion: energy, three components of the linear momentum, and three components of the angular momentum.
Application of distributions to the theory of elementary particles in quantum mechanics by Laurent Schwartz