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 11.1, Problem 11.6P
To determine
The second order in perturbation theory for the general case
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Check out a sample textbook solutionStudents have asked these similar questions
Problem #1
(Problem 5.3 in book). Come up with a function for A (the Helmholtz free energy) and
derive the differential form that reveals A as a potential:
dA < -SdT – pdV [Eqn 5.20]
1. Consider the 2D motion of a particle of mass u in a central force field with potential V(r).
a) Find the r, o polar-coordinate expression of the Lagrangian for this system and write down the
corresponding Euler-Lagrange e.o.m.s.
b) Note that the angular variable o is cyclic. What is the physical interpretation of the correspond-
ing integral of motion? (For the definitions of the italicized terms see this link.)
c) Solve for o in terms of this integral of motion and substitute the result into the Euler-Lagrange
equation for r. Show that the result can be arranged to look like a purely 1D e.o.m. of the form
dVef(r)
(1)
dr
Identify in the process the explicit expression for Vef(r), which will depend among other things on
the integral of motion.
d) Take now
k
V (r) =
with k > 0 to be an attractive electrostatic/gravitational-type potential. Sketch the profile of the
corresponding effective potential function Vef(r). Find the equilibrium solution for the correspond-
ing e.o.m. (1). What…
Q.n.3 A central force is defined to be a force that points radially, and whose magnitude depends on only
r. That is, F(r) = F(r) `r. Show that a central force is a conservative force, by explicitly showing that
Vx F = 0
Q.n.4 Consider two particles of masses ml and m2. Let m1 be confined to move on a circle of
O plane, centered at x = y = 0. Let m2 be confined to move on a circle of radius
radius a in the z =
b in the z = c plane, centered at x = y = 0. A light (massless) spring of spring constant k is attached
between the two particles.
a) Find the Lagrangian for the system.
Q.n.5 Oral Viva
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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