Monochromatic Radiation. Quantum Mechanics

As we learned with Fig. 8.2, nature provides radiation over a wavelength spectrum. The energy of monochromatic radiation is the monochromatic emissive power Ex, which we consider next. 

By definition, the relation between the monochromatic emissive power and the emissive power is 

This result (being temperature dependent after integration over the wavelength spectrum) proves that Enx = Ef,x (A., T). Here, we are interested in the explicit form of E x. Equation (8.22) implies that 

for the wavelength of isotropic waves we have (from the radius-volume relation of a sphere, for example) 

Classical electromagnetics and Boltzmann statistics, respectively, lead to explicit forms -of Eq. (8.29) for A - oc and A - 0. However, both theories fail to provide the explicit form for an arbitrary A. Extensive research for this explicit form eventually led Planck to the discovery of quantum mechanics, which explains radiation in terms of particles (photons) traveling with the speed of light. The energy and momentum associated with each photon, respectively, are 

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For studies in molecular physics, several characteristics of ultrafast laser pulses are of crucial importance. A fundamental consequence of the short duration of femtosecond laser pulses is that they are not truly monochromatic. This is usually considered one of the defining characteristics of laser radiation, but it is only true for laser radiation with pulse durations of a nanosecond (0.000 000 001s, or a million femtoseconds) or longer. Because the duration of a femtosecond pulse is so precisely known, the time-energy uncertainty principle of quantum mechanics imposes an inherent imprecision in its frequency, or colour. Femtosecond pulses must also be coherent, that is the peaks of the waves at different frequencies must come into periodic alignment to construct the overall pulse shape and intensity. The result is that femtosecond laser pulses are built from a range of frequencies the shorter the pulse, the greater the number of frequencies that it supports, and vice versa. 

From theoretical discussions involving the molecular eigenstates picture questions have arisen as to whether particular quantum mechanical interference effects can be observed by the use of suitably monochromatic radiation for excitation of the molecules 13>. (See Sect. 7.) Of course, it is also necessary to settle the controversies as to whether the BO or molecular eigenstates are correct, and if the former is indeed correct, which particular version of the BO approximation is to be employed for the calculation of nonradiative decay rates. 

There are technical causes characteristic to the instrument and collectively known as instrumental parameters width of entrance slit, quality of the optics, focal distance, diffraction phenomena through narrow orifices. However, there are also causes due to quantum mechanics, which ensure that the spectral transitions have a natural width . The radiations emitted by the atoms are not quite monochromatic. In particular with the plasmas, a medium in which the collision frequency is high (this reduces enormously the lifetimes of the excited states), Heisenberg s uncertainty principle plays a large role (Figure 14.7). Moreover, the elevated temperatures increase the speed of the atoms, enlarging line widths by the Doppler effect. Finally for all of these reasons, the width of the lines at 6000 K reaches several picometres. 

The inhomogeneous equation (2.114) is the quantum mechanical equivalent of the classical equation (2.41) and shows that the induced dipole moment of the atom interacting with a monochromatic radiation field behaves like a damped harmonic oscillator with the eigen frequency = (Ej - E )/h and a... 

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