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Consider a particle in the first excited state of an infinite square well of width L. This particle has wavefunction (found in image ) for −L/2 ≤ x ≤ L/2, and ψ2(x) = 0 elsewhere. a)  What is the value of the energy of this particle, E2? b)  What is the probability density function, ρ, for this particle? c)  At what values of x does the probability density vanish? d)  What is the probability of finding this particle in the interval 0 ≤ x ≤ L/8?

Consider a particle in the first excited state of an infinite square well of width L. This particle has wavefunction (found in image ) for −L/2 ≤ x ≤ L/2, and ψ2(x) = 0 elsewhere. a)  What is the value of the energy of this particle, E2? b)  What is the probability density function, ρ, for this particle? c)  At what values of x does the probability density vanish? d)  What is the probability of finding this particle in the interval 0 ≤ x ≤ L/8?

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter1: Getting Started
Section: Chapter Questions
Problem 48PQ: In 2011, artist Hans-Peter Feldmann covered the walls of a gallery at the New York Guggenheim Museum...
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Consider a particle in the first excited state of an infinite square well of width L. This particle has wavefunction

(found in image )

for −L/2 ≤ x ≤ L/2, and ψ2(x) = 0 elsewhere.

  1. a)  What is the value of the energy of this particle, E2?

  2. b)  What is the probability density function, ρ, for this particle?

  3. c)  At what values of x does the probability density vanish?

  4. d)  What is the probability of finding this particle in the interval 0 ≤ x ≤ L/8?

V₂(x) √ 2 sin 2πχ L
Transcribed Image Text:V₂(x) √ 2 sin 2πχ L
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