Eigenvalue plots Tannoudji's Quantum Mechanics Vol. II

1. Sep 23, 2009

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) ?

Last edited: Sep 23, 2009
2. Sep 23, 2009

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.

3. Sep 23, 2009

exciton

Thank you very much, it's all about detail