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 4.4, Problem 4.28P
To determine
The speed of a point on the equator. Whether the model make any sense or not.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
2.2 Express the following points in cylindrical and spherical coordinates:
(а) Р(1, — 4, —3)
(b) Q(3, 0, 5)
(c) R(-2, 6, 0)
Q.1) A particle of mass m moves in a central force field with pot ential V(r). The Lagrangian
in terms of spherical polar coordinat es (r, 0, ¢) is
L = m (r² + r*ô° + r² sin? 0ộ³) – V (r).
2
1. Find the momenta (p,, po, Pó) conjugate to (r, 0, ø).
2. Find the Hamiltonian H(r, 0, ¢, Pr, Po, Pø).
3. Write down the explicit Hamilton's equation of motion.
Solution:-
A curve in three dimensional space is parametrized as
F(u) = cos(u)i + sin(u)j + cos(3u)k,
и є [0, 2т).
Find the length of the curve (Hint: The answer is expressed in
terms of the elliptic integrals), and give a numerical value up to
three decimals (You can again use WolframAlpha).
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
- Convert points P(1,3,5), T(0, -4, 3), and S(-3,-4,-10) from Cartesian to cylindrical and spherical coordinates.arrow_forwardJ= , (r2 + 2)V () dr. find the value of J. Note that the divergence relation in spherical coordinates is given as follows V.v = r ar (sin@ ve) + r sin e ap r sin e aearrow_forwardUnder what conditions can we have VA = -HoJ? Prove the identity.arrow_forward
- Problem 3. A pendulum is formed by suspending a mass m from the ceiling, using a spring of unstretched length lo and spring constant k. 3.1. Using r and 0 as generalized coordinates, show that 1 L = = 5m (i² + r²0?) + mgr cos 0 – z* (r – lo)² 3.2. Write down the explicit equations of motion for your generalized coordinates.arrow_forwardIf H = 10 cos theta ar, evaluate integral H.dS over a hemisphere defined byr =1,0 < theta <2pie, 0 < phi < phi/2.arrow_forwardConsider the Kepler equation of motion M = E − e sin (E) Where : M – mean anomaly E – eccentric anomaly of an elliptic orbit e – eccentricity To find E, we need to solve the nonlinear equation: f(E) = M + e sin(E ) − E = 0 Given e = 0.0167 (Earth’s eccentricity)and M = 1 (in radians) compute E using a. Secant Method All with Ea ≤ 0.00001 To choose appropriate initial approximations or an interval containing the root, plot the function f(E) and then determine graphically where it crosses the E-axis.arrow_forward
- Problem 4.25 If electron, radius [4.138] 4πεmc2 What would be the velocity of a point on the "equator" in m /s if it were a classical solid sphere with a given angular momentum of (1/2) h? (The classical electron radius, re, is obtained by assuming that the mass of the electron can be attributed to the energy stored in its electric field with the help of Einstein's formula E = mc2). Does this model make sense? (In fact, the experimentally determined radius of the electron is much smaller than re, making this problem worse).arrow_forwardCalculate the divergences of cach of the following vectors: (a) v = 3k (b) v = r (c) = (4xz + y?) î + (12a² – 2²) ĵ + (xy – yz) k (d) ở = -yî+ x} (c) v = . -arrow_forwardA small sphere slides without friction on a smooth wire bent in the shape of acycloid (figure 2) whose parametric equation is: x =a( ϴ− sinϴ )y = a (1 + cos ϴ) Remark: A parametric equation is composed of the (x, y) coordinates of the system and is counted as asingle equation even if the coordinates are separated. Get the following for the above statement: a) Restriction equations. b) Number of degrees of freedom c) The kinetic energy of the system. d) The potential energy of the system e) The equations that describe the motion of the systemarrow_forward
- Consider a rectangular surface of length L and width W in the xy plane with its center at the origin: Which of the following are valid expressions for the area vector of this surface? Check all that apply. O (0,0, LW) O (W, L, 0) O (0,0, -LW) O (LW, LW, 0) O (0, LW, 0) O (L, W, 0)arrow_forwardLet E(r) : Calculate the line integral | E(r) - dr along the path a bc in the following two straight line segments: ra = (xa, Ya, 0), r, = (xa, Ye, 0), re = (xe, Ye, 0) %3D %3D with (ra, Ya) = ra(cos 0, sin 0), and (re, Ye) = re(cos 0, sin 0).arrow_forwardThe absolute value of the integral 5z3 + 3z2 dz, z2 – 4 over the circle |z – 1.5| = 1 in complex plane, is (up to two decimal places).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University 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 Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College 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