I Momentum eigenfunctions in an infinite well

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In an infinite potential well, the wavefunctions derived from the Schrödinger equation, sin(nπx/L), are not momentum eigenfunctions, leading to the conclusion that momentum cannot be directly measured in this scenario. The momentum operator is not self-adjoint within the confines of the well, which complicates the observability of momentum. Instead, the wavefunction represents a superposition of various momentum eigenstates, allowing for the possibility of measuring specific momentum values through probability distributions. Discussions also highlight that while momentum can theoretically take any value in quantum mechanics, relativistic constraints prevent infinite momentum in special relativity. Overall, the conversation emphasizes the complexities of momentum measurement in quantum systems, particularly within infinite potential wells.
  • #31
dyn said:
Are you telling me that in QM , CM and SR there is no limit on how big momentum can be ?
Yes, that's what they have told you.

dyn said:
Surely v not being able to reach c places a limit on momentum in SR
Instead of waving your hands, do the math. If you have questions about the math, you can start a new thread in the appropriate forum. This thread is closed as the question you asked in your OP has been answered.
 
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  • #32
dyn said:
Are you telling me that in QM , CM and SR there is no limit on how big momentum can be ? Surely v not being able to reach c places a limit on momentum in SR
It does not.
The momentum of a particle moving at speed ##v## is ##p=mv/\sqrt{1-(v^2/c^2)}##.

That value can be made as large as we please by choosing a value of ##v## sufficiently close to but still less than ##c##.
 
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