What are the eigenstates of a particle in a box whose bounds are [tex]x = -a/2[/tex] and [tex]x = a/2[/tex]?(adsbygoogle = window.adsbygoogle || []).push({});

Solution

Well, the eigenstates where [tex]x = 0, a[/tex] are just

[tex]\varphi_n = \sqrt{\frac{2}{a}} \sin \frac{n \pi x}{a}[/tex],

so why wouldn't the eigenstates just be

[tex]\varphi_n = \sqrt{\frac{2}{a}} \sin \frac{n \pi (x+a/2)}{a} = \sqrt{\frac{2}{a}}\sin \left(\frac{n \pi x}{a} + \frac{n \pi}{2}}\right)[/tex]

?

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# Homework Help: Particle in a Box Question

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