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Advanced Physics Homework Help
What Are the Eigenfunctions for the 1D Infinite Square Well?
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[QUOTE="andre220, post: 4944558, member: 487045"] [h2]Homework Statement [/h2] Find the ground and first excited state eigenfunctions of for the 1D infinite square well with boundaries -L/2 and +L/2 [h2]Homework Equations[/h2] $$\frac{-\hbar^2}{2m}\frac{\partial^2}{\partial x^2}\psi(x) = E\psi(x)$$ [h2]The Attempt at a Solution[/h2] Okay so I know how to solve it and get that $$\psi_1(x) = \sqrt{\frac{2}{L}}\cos{\frac{\pi x}{L}}$$. Next, I also know that $$\psi_2(x) = \sqrt{\frac{2}{L}}\sin{\frac{2\pi x}{L}}$$ one could reason this by arguing that each eigenfunction should have ##n-1## nodes. However, what is a more mathematical reasoning to ##\psi## for a given excited state. I am sure it is quite simple, I just can't seem to see it. [/QUOTE]
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What Are the Eigenfunctions for the 1D Infinite Square Well?
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