1. Consider a 1D particle of mass m subject to the harmonic potential given by:V(x) = mw²x² (b) Suppose now that the particle remains in the first excited state with ₁(r). Usingthe forms of the position and momentum operators defined in terms of the raisingand lowering operators, derive an expression for the uncertainty product ArAp. Howdoes your answer compare to the uncertainty product associated with the ground statewavefunction?For this question and the next you may find the following relations useful:and:p=iôn(2)=ħ2mw10,[â, a¹] = 1(a¹ + â)âyn(x) = √n+1+1(x)Fmw-(ât - â)√√n-1(2), if n>0if n = 0(2a)(2b)(3a)(3b)(3c)

Answered: Image /qna-images/answer/6aa4586b-d57d-4ef4-9bf1-30b969b81625.jpg

Answered: nd: H h 2mw (a¹ + a) (ât - â) Fmw p=i√…

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nd: H h 2mw (a¹ + a) (ât - â) Fmw p=i√ la ati a¹n(x) = √n+1vn+1(x) √√√n-1(2), if n>0 Ôn(2) = {√ if n = 0

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter28: Special Relativity

Section: Chapter Questions

Problem 62PE: (a) What is the effective accelerating potential for electrons at the Stanford Linear Accelerator,...

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Electromagnetic waves are waves that consist of magnetic field and electric field components perpendicular to each other. These field components are also perpendicular to the direction of propagation of the wave.

Question

1. Consider a 1D particle of mass m subject to the harmonic potential given by:
V(x) = mw²x²

(b) Suppose now that the particle remains in the first excited state with ₁(r). Using
the forms of the position and momentum operators defined in terms of the raising
and lowering operators, derive an expression for the uncertainty product ArAp. How
does your answer compare to the uncertainty product associated with the ground state
wavefunction?
For this question and the next you may find the following relations useful:
and:
p=i
ôn(2)=
ħ
2mw
10,
[â, a¹] = 1
(a¹ + â)
âyn(x) = √n+1+1(x)
Fmw
-(ât - â)
√√n-1(2), if n>0
if n = 0
(2a)
(2b)
(3a)
(3b)
(3c)

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