Finding the momentum uncertainty for a particle-in-a-box

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SUMMARY

The discussion focuses on calculating the momentum uncertainty (Δp) for an electron in a one-dimensional box, specifically using the normalized wave function ψ_n(x) = sqrt(2/L) * sin(nπx/L). The user seeks clarification on the momentum operator, which is defined as p = -iħ(d/dx). The correct approach involves calculating Δp using the formula Δp = sqrt( -

^2), where and

are evaluated using the wave function. The user is encouraged to proceed with the calculations based on this framework.

PREREQUISITES
  • Quantum mechanics fundamentals, specifically the particle-in-a-box model
  • Understanding of wave functions and normalization
  • Familiarity with operators in quantum mechanics, particularly the momentum operator
  • Knowledge of expectation values in quantum mechanics
NEXT STEPS
  • Calculate expectation values and

    for the nth excited state of the particle-in-a-box

  • Explore the implications of uncertainty principles in quantum mechanics
  • Study the derivation of the momentum operator in quantum mechanics
  • Investigate the relationship between wave functions and physical observables
USEFUL FOR

Students and professionals in quantum mechanics, particularly those studying wave functions and uncertainty principles in systems like the particle-in-a-box model.

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Homework Statement


I'm looking at an electron-in-a-box with walls at x=0 and x=L; I want to calculate the uncertainty (delta p) in the measurement of its momentum: sqrt(<p^2>−<p>^2) for its nth excited state.

Homework Equations


The normalized wave function: psi_n(x)=sqrt(2/L)*sin(n*pi*x/L)

The Attempt at a Solution


I'm not even sure what the p operator is for this situation. Should I just take p as -ihbar(d/dx) and sandwich p^2 and p like so? sqrt(<psi_n* | p^2 | psi_n> - <psi_n* | p | psi_n>^2)

Thanks in advance. I'll be online for a while; feel free to pop in here (http://cosketch.com/Rooms/euftgwf) if you can spare a few minutes to show me in real time.
 
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