1. A particle is confined in a region 0 ≤ x ≤ ∞ and has a wavefunction of the form Ne-xa (a) Normalize the wave function. (b) Find the average position of the article. (c) Find the average momentum of the particle. =
1. A particle is confined in a region 0 ≤ x ≤ ∞ and has a wavefunction of the form Ne-xa (a) Normalize the wave function. (b) Find the average position of the article. (c) Find the average momentum of the particle. =
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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![11:44
← SPHA031-23 Assignm...
SPHA031 Assignment No 3
o
Vo 4G+
LTE2 T
1. A particle is confined in a region 0≤x≤ ∞o and has a wavefunction of the form =
Ne-xa
|||
(a) Normalize the wave function.
(b) Find the average position of the article.
(c) Find the average momentum of the particle.
(d) Show that the uncertainties in position and momentum of the particle are given by
1
Ax = = and Ap = 0.
2a
2. The Heisenberg uncertainty principle demonstrate the symmetry between the particles
position and momentum. This can further be extended to the particles probability
amplitudes in position (x, t) and momentum (p, t). If y(x, t) =
1
√27th S dp (p, t)ex is the Fourier expansion of the probability amplitude for
position and (p,t)=√x 4(x, t)ex is its Fourier transform, prove that
+4(x, t) |² dx = +|ỹ(p,t)|²dp.
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd4a88a0-02bf-4e41-90d5-ab211b9ff461%2F38e86bcf-4ea5-4857-882f-8049e5730ca9%2F2w2tip_processed.jpeg&w=3840&q=75)
Transcribed Image Text:11:44
← SPHA031-23 Assignm...
SPHA031 Assignment No 3
o
Vo 4G+
LTE2 T
1. A particle is confined in a region 0≤x≤ ∞o and has a wavefunction of the form =
Ne-xa
|||
(a) Normalize the wave function.
(b) Find the average position of the article.
(c) Find the average momentum of the particle.
(d) Show that the uncertainties in position and momentum of the particle are given by
1
Ax = = and Ap = 0.
2a
2. The Heisenberg uncertainty principle demonstrate the symmetry between the particles
position and momentum. This can further be extended to the particles probability
amplitudes in position (x, t) and momentum (p, t). If y(x, t) =
1
√27th S dp (p, t)ex is the Fourier expansion of the probability amplitude for
position and (p,t)=√x 4(x, t)ex is its Fourier transform, prove that
+4(x, t) |² dx = +|ỹ(p,t)|²dp.
2
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