Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 4, Problem 4.75P
To determine
Show that
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Problem 3.7
(a) Suppose that f(x) and g(x) are two eigenfunctions of an operator Q, with
the same eigenvalue q. Show that any linear combination of f and g is itself
an eigenfunction of Q. with eigenvalue q.
(b) Check that f(x) = exp(x) and g(x) = exp(-x) are eigenfunctions of the
operator d?/dx², with the same eigenvalue. Construct two linear combina-
tions of f and g that are orthogonal eigenfunctions on the interval (-1, 1).
Prove that the vector V(x y .z)= 3y*z*i+ 4x°z²j+3x*y°(-k) is solenoidal.
k
4.2 Show that the vector field V(x, y,z)= o is irrotational using Vx V in cylindrical coordinates.
Problem 4.12 Calculate the potential of a uniformly polarized sphere (Ex. 4.2) directly from
Eq. 4.9.
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
Knowledge Booster
Similar questions
- A particle of mass m slides down in a smooth rigid bowl (hemispherical surface) as shown in Figure 3. R Figure 3. Derive for the particle the (a) Newtonian equations of motion, (b) Lagrange's equations of motion and the reaction of the bowl on m, and (c) Hamilton's equations of motion.arrow_forwardSuppose I have an operator A, and I discover that Â(2²) = 5 sinx and Â(sin x) = 5x². (a) Find Â(2² - sin x) (b) Name one eigenfunction and one eigenvalue of A.arrow_forwardSet up Lagrange’s equations in cylindrical coordinates for a particle of mass m in a potential field V (r, θ, z). Hint: v = ds/dt; write ds in cylindrical coordinates.arrow_forward
- Two particles, each of mass m, are connected by a light inflexible string of length l. The string passes through a small smooth hole in the centre of a smooth horizontal table, so that one particle is below the table and the other can move on the surface of the table. Take the origin of the (plane) polar coordinates to be the hole, and describe the height of the lower particle by the coordinate z, measured downwards from the table surface. i. sketch all forces acting on each mass ii. explain how we get the following equation for the total energyarrow_forwardLet f(x, y) = x² + 4y² and let C be the line segment from (0, 0) to (2, 2). You are going to compute là Vf. dr two ways: first, using the method learned in section 6.2 for с evaluating line integrals, and second, using the fundamental theorem for line integrals. First way: Vf=( C can be parameterized by r(t) = (t, Then '(t) and ▼ ƒ(r(t)) = { so sv. So 2 = [² = 2 - 1² || ( Vf. dr ▼ f(r(t)). r' (t)dt dt ). > > for 0 ≤ t ≤ 2. ).arrow_forwardProblem 2 Verify the Jacobi identity for Poisson brackets, {A, {B,C}} + {B, {C, A}} + {C, {A, B}} = 0 where the Poisson bracket is defined by n {X, Y} == Σ ΟΧ ΟΥ ΟΧ ΟΥ Әді дрі api əqi i=1 Here are the (canonical) coordinates, p; are the corresponding momenta, and n is the number of degrees of freedom.arrow_forward
- Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius a and positive charge q distributed evenly along its circumference. Imagine a small metal ball of mass m and negative charge −q0. The ball is released from rest at the point (0,0,d) and constrained to move along the z axis, with no damping. If 0<d≪a, what will be the ball's subsequent trajectory? repelled from the origin attracted toward the origin and coming to rest oscillating along the z axis between z=d and z=−d circling around the z axis at z=darrow_forwardA triangle in the xy plane is defined with corners at (x, y) = (0,0), (0, 2) and (4, 2). We want to integrate some function f(x, y) over the interior of this triangle. Choosing dx as the inner integral, the required expression to integrate is given by: Select one: o Sro S-o f(x, y) dx dy x=0 2y y=0 O S-o So F(x, y) dæ dy O o S f(x, y) dy dæ O So So F(x, y) dx dy x/2 =0arrow_forwardConsider the Laplace's equation u t uyy = 0 in the square 00 find the associated eigenfunctions X,(x) forn= 1,2,3, - c) Using the boundary condition calculate Y, y) d) Calculate the coefficients (c,) to satisfy the nonhomogeneous condition e) Write a formal series solution of the problem.arrow_forward
- Find the electric flux crossing the wire frame ABCD of length 1, width b and whose center is at a distance OP=d from an infinite line of charge with linear charge density λ. Consider that the plane of frame is perpendicular to the line OP (Fig. ). d Fig. A b D 8 . Carrow_forwardvative force, by explicitly showing that nds on only Q.n.4 Consider two particles of masses m1 and m2. Let ml be confined to move on a circle of radius a in the z = 0 plane, centered at x = y = 0. Let m2 be confined to move on a circle of radius 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 Vivaarrow_forwardSuppose that you have the Lagrangian L = 21 (;² + è°r2) + 420 for a 2D 20 system in plane polar coordinates (r, 0). Determine the pr and pe canonical coordinates.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON