An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter A.4, Problem 20P
To determine
To Find: The allowed values of
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For a particle in a 1-dimensional infinitely deep box of length L, the normalized wave function or the 1st excited state can be written as:
Ψ2(x) = {1/i(2L)1/2} ( eibx -e-ibx), where b = 2π/L.
Give the full expression that you need to solve to determine the probalibity of finding the particle in the 1st third of the box. Simplify as much as possible but do not solve any integrals.
The first four Hermite polynomials of the quantum oscillator areH0 = 1, H1 = 2x, H2 = 4x2 − 2, H3 = 8x3 − 12x.
Let p(x) = 12x3 − 8x2 − 12x + 7. Using the basis H = {H0, H1, H2, H3}, find the coordinate vector ofp relative to H. That is, find [p]H.
This is a textbook question, not a graded question
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?
Chapter A Solutions
An Introduction to Thermal Physics
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