Writing perturbed wave function

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SUMMARY

The discussion focuses on writing a perturbed wave function in quantum mechanics, specifically addressing the need for the perturbation parameter ##k^{(0)}## to maintain parity corresponding to the even and odd n-values of the original wave functions, ##sin(n \pi x)## for even n and ##cos(n \pi x)## for odd n. The user seeks clarification on whether ##k^{(0)}## must also adhere to this parity requirement. The conversation emphasizes the importance of using LaTeX for mathematical expressions in forum posts.

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Hello,

I'm trying to write a wave function for a perturbed system. The original (unperturbed) wave function has two solutions for even and odd n-values, for example ##sin(n \pi x)## for even-n and ##cos(n\pi x)## for odd-n. Then, the perturbed wave function also has an even and odd solutions. My question is does ##k^{(0)}## in the attachment also need to be even or odd according to even and odd n-values?Thanks!
 

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    perturbed.PNG
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