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
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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1. Consider a 1D particle of mass m subject to the harmonic potential given by:
V(x) = mw²x²
Transcribed Image Text: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)
Transcribed Image Text:(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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