Normal Coordinates in Quantum Mechanics

Normal Coordinates in Quantum Mechanics.—It can be shown2 that when the coefficients Bki of Equation 37-14 are determined in the manner described in the last section, the introduction of the transformation 37-14 for the Qk s into the expression for the potential energy yields the result 

These properties of the normal coordinates enable us to treat the problem of the vibrations of polyatomic molecules by the methods of quantum mechanics. 

1 This becomes five for linear molecules, which have only two degrees of rotational freedom. 

2 For a proof of this see E. T. Whittaker, Analytical Dynamics, Sec. 77, Cambridge University Press, 1927. 

3 A transformation which leaves a simple sum of squares unaltered is called an orthogonal transformation. 

---