Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Question
Chapter 4.2, Problem 4.14P
(a)
To determine
First four Laguerre polynomials using equation 4.88.
(b)
To determine
Value of
(C)
To determine
Value of
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Students have asked these similar questions
Divergence theorem. (a) Use the divergence theorem to prove,
v = -478 (7)
(2.1)
(b) [Problem 1.64, Griffiths] In case you're not persuaded with (a), try replacing r by (r² + e²)2
and watch what happens when ɛ → 0. Specifically, let
1
-V².
4л
1
D(r, ɛ)
(2.2)
p2 + g2
By taking note of the defining conditions of 8°(7) [(1) at r = 0, its value goes to infinity, (2) for
all r + 0, its value is 0, and (3) the integral over all space is 1], demonstrate that 2.2 goes to
8*(F) as ɛ → 0.
Problem 2.11
(a) Compute (x). (p). (x²), and (p²), for the states yo (Equation 2.60) and 1 (Equation
2.63), by explicit integration. Comment: In this and other problems involving the
harmonic oscillator it simplifies matters if you introduce the variable = √mo/hx
and the constanta (m/h)¹/4
(b) Check the uncertainty principle for these states.
(c) Compute (T) and (V) for these states. (No new integration allowed!) Is their sum
what you would expect?
Show that if (h|ệh) = (Ôh\h) for all functions h (in Hilbert space),
then (flÔg) = (Ôf\g) for all f and g (i.e., the two definitions of "hermi-
tian"-Equations 3.16 and 3.17-are equivalent). Hint: First let h = f+ 8, and
then let h = f + ig.
(SIÊF) = (Ô ƒIS) for all f(x).
[3.16]
(FIÔg) = (Ô ƒ\g) for all f (x) and all g(x).
[3.17]
Chapter 4 Solutions
Introduction To Quantum Mechanics
Ch. 4.1 - Prob. 4.1PCh. 4.1 - Prob. 4.3PCh. 4.1 - Prob. 4.4PCh. 4.1 - Prob. 4.5PCh. 4.1 - Prob. 4.6PCh. 4.1 - Prob. 4.7PCh. 4.1 - Prob. 4.8PCh. 4.1 - Prob. 4.9PCh. 4.1 - Prob. 4.10PCh. 4.1 - Prob. 4.11P
Ch. 4.2 - Prob. 4.12PCh. 4.2 - Prob. 4.13PCh. 4.2 - Prob. 4.14PCh. 4.2 - Prob. 4.15PCh. 4.2 - Prob. 4.16PCh. 4.2 - Prob. 4.17PCh. 4.2 - Prob. 4.18PCh. 4.2 - Prob. 4.19PCh. 4.2 - Prob. 4.20PCh. 4.3 - Prob. 4.21PCh. 4.3 - Prob. 4.22PCh. 4.3 - Prob. 4.23PCh. 4.3 - Prob. 4.24PCh. 4.3 - Prob. 4.25PCh. 4.3 - Prob. 4.26PCh. 4.3 - Prob. 4.27PCh. 4.4 - Prob. 4.28PCh. 4.4 - Prob. 4.29PCh. 4.4 - Prob. 4.30PCh. 4.4 - Prob. 4.31PCh. 4.4 - Prob. 4.32PCh. 4.4 - Prob. 4.33PCh. 4.4 - Prob. 4.34PCh. 4.4 - Prob. 4.35PCh. 4.4 - Prob. 4.36PCh. 4.4 - Prob. 4.37PCh. 4.4 - Prob. 4.38PCh. 4.4 - Prob. 4.39PCh. 4.4 - Prob. 4.40PCh. 4.4 - Prob. 4.41PCh. 4.5 - Prob. 4.42PCh. 4.5 - Prob. 4.43PCh. 4.5 - Prob. 4.44PCh. 4.5 - Prob. 4.45PCh. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - Prob. 4.48PCh. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - Prob. 4.51PCh. 4 - Prob. 4.52PCh. 4 - Prob. 4.53PCh. 4 - Prob. 4.54PCh. 4 - Prob. 4.55PCh. 4 - Prob. 4.56PCh. 4 - Prob. 4.57PCh. 4 - Prob. 4.58PCh. 4 - Prob. 4.59PCh. 4 - Prob. 4.61PCh. 4 - Prob. 4.62PCh. 4 - Prob. 4.63PCh. 4 - Prob. 4.64PCh. 4 - Prob. 4.65PCh. 4 - Prob. 4.66PCh. 4 - Prob. 4.70PCh. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Prob. 4.75PCh. 4 - Prob. 4.76P
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