Eigenvalue plots Tannoudji's Quantum Mechanics Vol. II

[exciton]

Hi guys,

probably that's the wrong forum, but I was just curious about
the plot (Figure 1 Chapter XI A./1. page 1097 / Volume II) of the eigenvalues

$$E(\lambda)$$.

If I calculate them they are supposed to be straight lines with positive or
negative slope i.e.:

$$E(\lambda) = E_n^0 + \lambda \epsilon_1^j$$

in first order perturbation theory.

Am I missing s.th. or are these curves just ment to be realistic measurement curves
(and if so why isn't there any hint in the text) ?

 

[xepma]

If you calculate higher order corrections to the energy you will also have term of order $$\lambda^2$$ and higher. So the exact value of E(lambda) is not given by a straight line, but some curve instead. The plot gives an example of what the exact value of E(lambda) might be.

 

[exciton]

Thank you very much, it's all about detail