Solving 12.10 Zwiebach: Different Basis States?

[ehrenfest]

Homework Statement

For Quick Calculation 12.10, when Zwiebach says that the basis states are different, does he mean their ground states, i.e. p^+ and p_T are different or that their \lambda_{n,I} or either?

I think that if the p^+ and p_T are different then it is trivial because of 12.184.

Homework Equations

The Attempt at a Solution

 

[malawi_glenn]

You seem to have many question from this book, is this coursework? You have a teacher in this course?