Introduction To Quantum Mechanics
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 11.6P
To determine

The second order in perturbation theory for the general case ca(0)=a,cb(0)=b .

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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
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