27 : 2/ Quantum Mechanical Basis of Molecular Spectra 



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Equation 4 will be valid. Another canonically conjugate pair of 

 variables are energy E and time t. Again, one may write an inequality ; 

 for those variables it is 



* (4') 



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This states that if one describes an atom or molecule in terms of its exact 

 energy, it is impossible to tell when it had this energy. 



Table I illustrates the application of the uncertainty principle to 

 two large particles, a piece of chalk and a bacterium, Escherichia coli, 

 and to two subatomic particles, a neutron and an electron. The 

 location of the edge of the chalk and of the E. coli are uncertain to the 

 order of one interatomic distance. The neutron's location is known 

 only in that it may be restricted to a region within an atomic nucleus. 

 A rather hypothetical calculation shows the results of attempting to 

 restrict the electron to the atomic nucleus; the calculation shows this is 

 absurd because the uncertainty in the electron's velocity would be 

 greater than the velocity of light. This is one of several lines of evidence 

 indicating that one cannot know the position of the electron this precisely. 



TABLE I 



Examples Illustrating the Uncertainty Principle 



Mass | Ax | \Ap\ = h/\Ax\ Av = Ap/m 



Item Mass in gm in amu* in cm in gm c/sec in cm/sec Uncertainty 



The uncertainties in the momenta of the chalk or even of the E. coli 

 cannot be experimentally detected. By way of contrast, the uncer- 

 tainties in the velocities of the electron within an atom or the neutron 

 within a nucleus are of major importance. The uncertainty Av for the 

 neutron is one-fiftieth the velocity of light. 



In addition to the correspondence and uncertainty principles, there 

 are other general conclusions basic to quantum mechanics which can be 

 derived by the mathematically adept. One of the more important of 

 these is the existence of characteristic (or eigen-) functions. With the eigen- 

 functions, there are associated eigenvalues of the variables described by 



