Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 2.2, Problem 2.4P
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Find the normalization constant A [in Equation Ψ(x, y, z) = A sin(k1x)sin(k2y)sin(k3z) ] for the first excited state of a particle trapped in a cubical potential well with sides L. Does it matter which of the three degenerate excited states you consider?
where
and
kyk₂
I
2
k
2m E
2
ħ²
2m
ħ²
(V-E)
3 Show that the solutions for region II
can also be written as
2/₁₂ (²) = Ccas (₁₂²) + D sin (k₂²)
for Z≤ 1W/
4 Since the potential well Vez) is symmetrical,
the possible eigen functions In You will
be symmetrical, so Yn will be either
even or odd.
a) write down the even solution for
region. II
b) write down the odd solution
region
for
on II
In problem 2, explain why A=G=0₁
Assume that you have a quantum mechanical observable N with eigenvalues
Wi and corresponding eigenvectors |w;). Show that
(n?) – (N)²
where P(w;) is the probability of measuring the eigenvalue w; for some quantum state.
Chapter 2 Solutions
Introduction To Quantum Mechanics
Ch. 2.1 - Prob. 2.1PCh. 2.1 - Prob. 2.2PCh. 2.2 - Prob. 2.3PCh. 2.2 - Prob. 2.4PCh. 2.2 - Prob. 2.5PCh. 2.2 - Prob. 2.6PCh. 2.2 - Prob. 2.7PCh. 2.2 - Prob. 2.8PCh. 2.2 - Prob. 2.9PCh. 2.3 - Prob. 2.10P
Ch. 2.3 - Prob. 2.11PCh. 2.3 - Prob. 2.12PCh. 2.3 - Prob. 2.13PCh. 2.3 - Prob. 2.14PCh. 2.3 - Prob. 2.15PCh. 2.3 - Prob. 2.16PCh. 2.4 - Prob. 2.17PCh. 2.4 - Prob. 2.18PCh. 2.4 - Prob. 2.19PCh. 2.4 - Prob. 2.20PCh. 2.4 - Prob. 2.21PCh. 2.5 - Prob. 2.22PCh. 2.5 - Prob. 2.23PCh. 2.5 - Prob. 2.24PCh. 2.5 - Prob. 2.25PCh. 2.5 - Prob. 2.26PCh. 2.5 - Prob. 2.27PCh. 2.5 - Prob. 2.28PCh. 2.6 - Prob. 2.29PCh. 2.6 - Prob. 2.30PCh. 2.6 - Prob. 2.31PCh. 2.6 - Prob. 2.32PCh. 2.6 - Prob. 2.34PCh. 2.6 - Prob. 2.35PCh. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 2 - Prob. 2.38PCh. 2 - Prob. 2.39PCh. 2 - Prob. 2.40PCh. 2 - Prob. 2.41PCh. 2 - Prob. 2.42PCh. 2 - Prob. 2.44PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Prob. 2.47PCh. 2 - Prob. 2.49PCh. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - Prob. 2.52PCh. 2 - Prob. 2.53PCh. 2 - Prob. 2.54PCh. 2 - Prob. 2.58PCh. 2 - Prob. 2.63PCh. 2 - Prob. 2.64P
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