504 Quantum Mechanical Basis of Molecular Spectra /27 : 2 



motion, although a large aggregate of these small particles will appear, 

 on the average, to behave as predicted by Newtonian mechanics. The 

 individual particles move in such a manner that only the relative 

 probability of their being at a certain place can be described. This 

 relative probability is given by the square of the amplitude of a mathe- 

 matical expression called a wave function. The general theory which 

 predicts this behavior is called quantum mechanics. 



Quantum mechanics has been verified by a wide variety of phenom- 

 ena. These involve measurements of specific heats, entropies, 

 behavior of gases in discharge tubes, magnetic experiments, and inter- 

 actions of atomic particles, as well as the characteristic spectra associated 

 with atoms and molecules. Modern quantum mechanics leads to the 

 picture of an atom consisting of a small (about 10 ~ 12 cm diameter), 

 heavy, positively charged nucleus surrounded by a smeared out cloud of 

 electrons. Within the nucleus of the atom are the protons and neutrons. 

 The electrons cannot be pinpointed at any spot or orbit, but they spend 

 a greater amount of time in certain most probable regions called orbitals. 

 (Similarly, it is impossible to specify their instantaneous momentums or 

 energies.) There is a certain region within which there is close to 

 1 00 per cent probability of finding all the electrons associated with a 

 given nucleus. This region constitutes the atom; it has a diameter of 

 the order of 10~ 8 cm (1 A). 



The indeterminancy and peculiar effects of quantum mechanics 

 apply only to very small particles. One of the fundamental principles 

 which any quantum mechanical statement must obey is that when 

 applied to large masses, high energies, and long times, quantum 

 mechanics reduces to (or corresponds to) the laws of classical physics. 

 This is known as the correspondence principle; it is important for an 

 intuitive grasp of quantum mechanics as well as for a complete mathe- 

 matical analysis. 



Quantum mechanics, when formulated in the symbolism of mathe- 

 matics, can be shown to lead directly to another general principle, the 

 so-called (Heisenberg) uncertainty principle. It states that there exist 

 various pairs of variables (called canonically conjugate variables) which 

 cannot both be known precisely simultaneously. For example, if A# 

 indicates the uncertainty about the location of a particle, and /S.p the 

 uncertainty concerning its momentum, then the uncertainty principle 

 states that the product of the absolute values obeys the inequality 



|A*| |A/,| > A (4) 



ATT 



In other words, no matter how one goes about measuring the location x 

 of the particle, the measurement will alter the momentum p so that 



