Formula- first order correction to the n-th wave func

[Imperatore]

Could anybody explain me why indeed we can express the first-order correction to the n-th wave function $$\psi_{n}^{1}$$ by linear combination $$\sum_{m} c_{m}^{(n)}\psi_{m}^{o}$$

 

[mfb]

The $\psi_n$ (if defined properly - you didn't specify where they come from) are a base of your vector space of wave functions. You can express every physical wave function with such a linear combination.

 

[Imperatore]

you didn't specify where they come from

It's Schrödinger equation to first order $$\lambda^{1}$$ You can see it on page 224 in the Griffiths' Introduction to quantum mechnics

 

[Imperatore]

So I am curious, how we can expand the 2-nd order correction to the wave function ? ;)

http://iate.oac.uncor.edu/~manuel/libros/Modern%20Physics/Quantum%20Mechanics/

 

[mfb]

That page doesn't load.

In a similar way, but the equations get progressively more messy with each order. I don't have the book here.