A More General Variation Method

A More General Variation Method.—A method has been devised1 which gives both an upper and a lower limit for an energy level. If we represent by E and D the integrals 

There will be some energy level Wk which lies at least as near E as any other, i.e., for which 

From this we see that the condition in Equation 26-27 applies to both cases. 

The application of this method to actual problems of the usual type is more difficult than that of the simple variation method because, in addition to the integral E, it is necessary to evaluate D, which ordinarily is considerably more difficult than E. 

It may be pointed out that by varying parameters in a function in such a way as to make A a minimum the function is made to approach some correct wave function pk as closely as is permitted by the form of l . This method consequently may be considered as another type of variation method applicable to any state of a system. 

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