704 X. ON THE STRUCTURE OF 'MATTER' |
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We should notice that the dynamical triplet of impulse co-ordinates occurs conjointly with the geometrical triplet of the co-ordinates of position. The second law of motion tells us that 'the change in momentum is proportional to the impressed force and takes place in the direction in which that force acts'. If we assume that the force
K is derivable from the potential energy E(a_{po}t, kinetic energy is expressed as a function of the g.'j and their derivatives the g.'s.
To help visualization we can construct and consider the
p and q as rectangular co-ordinates in two dimensions in the phase plane of our system. In this plane the sequence of those graph-points that correspond to the successive states of motion of the system represent the phase paths or phase-orbits. The characteristic structural feature of the quantum theory is that it selects a discrete family of phase-orbits from the infinity of possible orbits.We next consider a point-mass
m that is bound elastically to its position of rest, and which can move to either side of the central position only in the direction, or its reverse, when experiencing a restoring force. We call suchpoint-mass a linear oscillator. If we wish to emphasize that our oscillator is capable only of definite vibrations, on account of its elastic attachment, we call it a 'harmonic oscillator'. If the vibration number, or the frequency of the oscillator, which is represented by the number of its free vibrations per unit of 'time', is denoted by v, then the vibration is represented by |
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