How are wavefunctions and eigenkets used differently in quantum mechanics?

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Wavefunctions and eigenkets represent different approaches in quantum mechanics, with wavefunctions typically used in non-relativistic contexts while eigenkets are favored in more abstract formulations. Wavefunctions are coefficients in a state's expansion in the position basis, allowing operators to act on them to produce new functions, as seen with momentum operators. The discussion highlights the confusion arising from these differing methodologies, emphasizing that while wavefunctions are more concrete and intuitive for calculations, eigenkets provide a more rigorous theoretical framework. Understanding the mathematical foundations, such as Gleason's theorem and the role of observables, is crucial for grasping these concepts. Ultimately, both approaches have their merits, and familiarity with each can enhance comprehension of quantum mechanics.
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micromass said:
Don't excuse yourself for asking. We are here to answer questions like yours!

But yes, ##\psi(x)## is a scalar, so you can treat it like one.

The wavefunction ##\psi## itself must be treated as a vector.

Thank you for your help!
 

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