By Laurent Schwartz
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Additional resources for Application of distributions to the theory of elementary particles in quantum mechanics
21) We speak of an emission “line” of width ν. 21) in the form ν· t≈ 1 . 22) In this form the relation has a general validity for pulses of finite duration; we must assume, however, that the phase of the electric field does not change significantly within t. 22) can become considerably larger than 1/2π . In general, the relation has to be understood in such a way that it defines the minimum value of the linewidth for a pulse of finite duration. 22) is that the Fourier decomposition of a pulse in a spectral apparatus leads to partial waves which, due to their smaller frequency widths, are considerably longer than the incident wave.
Our example of an ensemble of identical atoms illustrates nicely the disturbing effects of a measurement on a system’s dynamics. Let us assume that the atoms are initially in the lower state 1. The intense coherent field induces a transition from 1 to 2, and the theory states that – in the case of resonance – at a certain moment t A , all the atoms are with certainty in the excited state 2. e. which level they are in. Our curiosity has dramatic consequences: the corresponding measurement leads to an abrupt interruption of the coherent interaction with the external field, and each of the atoms – according to the probability determined by the wave function at the corresponding instant – is put into either the initial or the excited state.
Let us consider, for instance, linearly polarized light and ask which circular polarization is present. Our answer is that because linearly polarized light can be considered as a superposition of a left handed circularly and a right handed circularly polarized wave, both polarizations are simultaneously present with equal probability. ” In fact, the electric field strength as the primary physical variable in the above example is well defined with respect to magnitude and direction at each moment, and we arrive at the conclusion that one physical variable has simultaneously different values only when questions of the type: What happens when light is passing through a spectral apparatus?