Prove Uncertainity Relation for Particle in a Box w/ Length L

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SUMMARY

The discussion centers on proving the Heisenberg Uncertainty Relation for a particle in a box of length L, specifically the inequality ΔxΔp ≥ h/(4π). The participant expresses concern about the logical nature of the question, suggesting it resembles a circular argument. They emphasize the need to calculate the expectation values of position (x) and momentum (p) separately before multiplying them to validate the uncertainty relation without invoking the principle itself, which would be circular reasoning.

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  • Understanding of quantum mechanics principles, particularly the Heisenberg Uncertainty Principle.
  • Familiarity with expectation values in quantum mechanics.
  • Knowledge of wave functions and their properties in a one-dimensional box.
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  • Study the derivation of the Heisenberg Uncertainty Principle in quantum mechanics.
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string_theory
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Hi dear virtual friends,

I am now going to ask you something. I would be pleased if you would answer me.

In an exam I was asked to show that for a particle in a box of width length L , delta (x)delta(p)>=h/(4*pi) holds.
I think this is not a logical question. Because I think it is like asking something like this: Prove A using A.

I would be really grateful if you would write something regarding this.
Thank you.

P.S. My problem is not envolving you in doing my homework. I just wanted to know if what I think is right or wrong.
 
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i think you were supposed to calculate Δx and Δp separately, then multiply the two together, and compare it to h/4pi.

you know, find the expectation value of x, and then the expectation value of x2 and all that jazz.

of course you are not allowed to use the Heisenberg Uncertainty principle to show that the Heisenberg Uncertainty principle is true. that is circular.
 
Thank you very much for youranswer.
 

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