Note that the way I have written the "transitions" above is translated in terms of the matrix elements x_(m,n) as follows (taking the example of 1) ):
1) (n-1) -> n -> (n+1) -> n is x_(n-1,n) x_(n,n+1) x_(n+1,n)
and the same for the other two.
And for the last part of the problem, if...
For the matrix element (x^3)_(n-1,n), you have to consider the following 3 possible "transitions":
1) (n-1) -> n -> (n+1) -> n
2) (n-1) -> (n-2) -> (n-1) -> n
3) (n-1) -> n -> (n-1) -> n
The contribution to (x^3)_(n-1,n) are as follows (all of the following are multiplied by
[hbar/(2 m...
Actually, I was wrong about the reasoning why you need two conditions. In the above inequality, it is just because that is all you need to satisfy the inequality (which is quadratic in x = delta_S). In addition, the extra condition you get from using x = delta_V can be transformed to 21.3...
There are two variables that are being varied arbitrarily (del_S and del_V). So you will only need to satisfy TWO conditions. The following is one way to derive one set of two conditions:
In the inequality (21.2) of pg 64, let x = delta_S (just for convenience;)
Now you get a quadratic...