Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 11.1, Problem 11.2P
To determine
The all four matrix elements
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Starting with the equation of motion of a three-dimensional isotropic harmonic
ocillator
dp.
= -kr,
dt
(i = 1,2,3),
deduce the conservation equation
dA
= 0,
dt
where
1
P.P, +kr,r,.
2m
(Note that we will use the notations r,, r2, r, and a, y, z interchangeably, and similarly
for the components of p.)
Consider the function
v(1,2) =(
[1s(1) 3s(2) + 3s(1) 1s(2)]
[x(1) B(2) + B(1) a(2)]
Which of the following statements is incorrect concerning p(1,2) ?
a.
W(1,2) is normalized.
Ob.
The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons.
OC.
y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with
eigenvalue = -5 hartree.
d.
The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit.
Oe.
The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.
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
Chapter 11 Solutions
Introduction To Quantum Mechanics
Ch. 11.1 - Prob. 11.1PCh. 11.1 - Prob. 11.2PCh. 11.1 - Prob. 11.3PCh. 11.1 - Prob. 11.4PCh. 11.1 - Prob. 11.5PCh. 11.1 - Prob. 11.6PCh. 11.1 - Prob. 11.7PCh. 11.1 - Prob. 11.8PCh. 11.1 - Prob. 11.9PCh. 11.3 - Prob. 11.10P
Ch. 11.3 - Prob. 11.11PCh. 11.3 - Prob. 11.12PCh. 11.3 - Prob. 11.13PCh. 11.3 - Prob. 11.14PCh. 11.3 - Prob. 11.15PCh. 11.3 - Prob. 11.16PCh. 11.4 - Prob. 11.17PCh. 11.5 - Prob. 11.18PCh. 11.5 - Prob. 11.19PCh. 11.5 - Prob. 11.20PCh. 11.5 - Prob. 11.21PCh. 11.5 - Prob. 11.22PCh. 11 - Prob. 11.23PCh. 11 - Prob. 11.24PCh. 11 - Prob. 11.25PCh. 11 - Prob. 11.26PCh. 11 - Prob. 11.27PCh. 11 - Prob. 11.28PCh. 11 - Prob. 11.29PCh. 11 - Prob. 11.30PCh. 11 - Prob. 11.31PCh. 11 - Prob. 11.33PCh. 11 - Prob. 11.35PCh. 11 - Prob. 11.36PCh. 11 - Prob. 11.37P
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