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gremory
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- TL;DR Summary
- Power series to solving the infinite square well
Just earlier today i was practicing solving some ODEs with the power series method and when i did it to the infinite square well i noticed that my final answer for ##\psi(x)## wouldn't give me the quantised energies. My solution was
$$\psi(x) = \sum^{\infty}_{n=0} k^{2n}(\cos(x) + \sin(x))$$, with ##k = \frac{\sqrt{2mE}}{\hbar}##. I want to know what's the catch when doing this because we need the boundary conditions to quantize the energies and with this solution i don't see how i would get that.
$$\psi(x) = \sum^{\infty}_{n=0} k^{2n}(\cos(x) + \sin(x))$$, with ##k = \frac{\sqrt{2mE}}{\hbar}##. I want to know what's the catch when doing this because we need the boundary conditions to quantize the energies and with this solution i don't see how i would get that.
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