This is an introductory question related to expectation values and the Heisenberg Uncertainty Principle.
A particle is in a one-dimensional dimensionless harmonic oscillator potential
[ - (d/dx)^{2} + x^{2} ] Psi = E Psi.
The states shown are normalized. Shown is Psi^{ }and the results of the integrals that give <x> and <x^{2}> <p> and <p^{2}> (which are by convention are unitless). Vary n from 1 to 10.
In this dimensionless case, hbar=1. What other constants---or group of constants---must be set equal to one?
What do you notice about <x> and <x^{2}> and <p> and <p^{2}>?
Calculate DxDp for n=0. What do you notice considering hbar=1?
What is E_{n}? How does this agree with or disagreee with the standard case for the harmonic oscillator?
How much KE and how much PE?
Script by Mario Belloni.
Questions by Mario Belloni.
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