2. A particle of mass, m, has the wavefunction given by: (x,t) = Ce-a[(mx²/h) + it] . (a) Sketch Re [(x,0)] as a function of x. (b) Sketch Re [p(0, t)] as a function of t. (c) Sketch the probability density for finding the particle at x at t = 0. (d) Explain the time dependence in the probability density for locating the particle in space. (e) Find C

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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2. A particle of mass, m, has the wavefunction given by: (x, t) = Ce-a[(mx²/h) + it] .
(a) Sketch Re [(x,0)] as a function of x.
(b) Sketch Re [p(0, t)] as a function of t.
(c) Sketch the probability density for finding the particle at x at t = 0.
(d) Explain the time dependence in the probability density for locating the particle in space.
(e) Find C
(f) Find (x)
(g) Find (x2)
(h) Find ox
(i) Find (p)
(j) Find (p?)
(k) Find op
(1) Is the product, O,0, consistent with the Heisenberg uncertainty principle?
(m) Find T
Transcribed Image Text:2. A particle of mass, m, has the wavefunction given by: (x, t) = Ce-a[(mx²/h) + it] . (a) Sketch Re [(x,0)] as a function of x. (b) Sketch Re [p(0, t)] as a function of t. (c) Sketch the probability density for finding the particle at x at t = 0. (d) Explain the time dependence in the probability density for locating the particle in space. (e) Find C (f) Find (x) (g) Find (x2) (h) Find ox (i) Find (p) (j) Find (p?) (k) Find op (1) Is the product, O,0, consistent with the Heisenberg uncertainty principle? (m) Find T
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