The uncertainties of a position and a momentum of a particle (Ax) and (Ap) aredefined asAx = /(x²) – (x)²Ap = /(p*) – {p}²1. For the particle in the box at the ground eigenstate (n = 1) and first excited state (2), what is the uncertainty in the value x? How would you interpret theresults of these calculations?n =2. For the particle in the box at the ground eigenstate (n = 1) and first excited state (n = 2), what is the uncertainty in the value p? How would you interpret theresults of these calculations?3. What is the product for the ground and first excited state: AxAp.4. Does the Heisenberg Uncertainty Principle hold for a particle in each of thesestates?

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The uncertainties of a position and a momentum of a particle (Ax) and (Ap) a defined as are

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Question

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The uncertainties of a position and a momentum of a particle (Ax) and (Ap) are
defined as
Ax = /(x²) – (x)²
Ap = /(p*) – {p}²
1. For the particle in the box at the ground eigenstate (n = 1) and first excited state (
2), what is the uncertainty in the value x? How would you interpret the
results of these calculations?
n =
2. For the particle in the box at the ground eigenstate (n = 1) and first excited state (
n = 2), what is the uncertainty in the value p? How would you interpret the
results of these calculations?
3. What is the product for the ground and first excited state: AxAp.
4. Does the Heisenberg Uncertainty Principle hold for a particle in each of these
states?

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