Formal Development of the Theory for Nondegenerate States

Chapter 12 Time-Independent Rayleigh-Schrddinger Perturbation Theory 

It is clear that, when X = 0, then H = Ho, , = i/f,- and Wj = Ej. As X is increased from zero, Wi and / , change in (we expect) a continuous way. In other words, Wi and 4 i are continuous functions of the variable parameter X, and they are known at the particular value X = 0. Therefore, we can expand them as series in powers of X about the point X = 0. Thus, for a given state 

Here we must remember that X is a variable and etc. are constants. The 

XwP (which is just wy after X is set equal to unity) is the first-order correction to 

In precisely the same manner, we can expand the unknown eigenfunction as a power series in A  

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Section 12-2 Formal Development of the Theory for Nondegenerate States... 

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