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

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The discussion centers on proving the uncertainty relation for a particle in a box of length L, specifically that delta(x)delta(p) ≥ h/(4π). The original poster expresses concern that the question seems circular, akin to proving a principle using itself. They suggest that the solution involves calculating the expectation values of position and momentum separately before comparing the product to h/4π. It is emphasized that using the Heisenberg Uncertainty Principle to validate itself would be a logical fallacy. The conversation highlights the need for a mathematical approach to demonstrate the uncertainty relation without circular reasoning.
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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.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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