Finding the expected value of position in a Potential Well

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The discussion revolves around a homework problem involving an electron in a potential well, where the user has solved the Schrödinger Equation but struggles with determining the correct wave function. They initially obtained a complex exponential solution, which does not satisfy boundary conditions, leading to confusion about symmetric (cosine) and asymmetric (sine) solutions. The user attempts to compute the expected value of (z-<z>)², simplifying it to <z²>, but encounters discrepancies between their results and the textbook's answers. The conversation emphasizes the importance of correctly applying boundary conditions and normalization in quantum mechanics to achieve accurate solutions.
  • #31
ja07019 said:
Okay you say that this is only half of the solution
And that only for ##|z|\le L/2##. The wave function is nonzero there and contributes to ##<z^2>##.

I'm not a textook. Read this from cover to cover. We (you) can't spend weeks on this topic.
 
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  • #32
BvU said:
And that only for ##|z|\le L/2##. The wave function is nonzero there and contributes to ##<z^2>##.

Okay just one more question then, if the wavefunction is piecewise, how would you come up with the expected values? Does that require a transform?
 

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