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 11.1, Problem 11.7P
To determine
The value of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
For Problem 8.16, how do I prove the relations and give the correct expressions?
The dynamics of a particle moving one-dimensionally in a potential V (x)
is governed by the Hamiltonian Ho = p²/2m + V (x), where p =
is the momentuin operator. Let E, n =
of Ho. Now consider a new Hamiltonian H
given parameter. Given A, m and E, find the eigenvalues of H.
-ih d/dx
1, 2, 3, ... , be the eigenvalues
Ho + Ap/m, where A is a
%3|
I have been trying this problem for a while and I am stuck. I tried doing some integrals after doing the cross product, but nothing seems to be working.
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
Knowledge Booster
Similar questions
- The radial force is given as F = (-k/r^2) r^. A) Is this force stable? B) If part A is positive, find the potential function. For F to be stable, its tau must be zero.I want you to calculate its tau and obtain the potential function through the Stokes theorem.arrow_forwardConsider 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_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
- A point particle moves in space under the influence of a force derivablefrom a generalized potential of the formU(r, v) = V (r) + σ · L,where r is the radius vector from a fixed point, L is the angular momentumabout that point, and σ is the fixed vector in space. Find the components of the force on the particle in spherical polar coordinates, on the basis of the equation for the components of the generalized force Qj: Qj = −∂U/∂qj + d/dt (∂U/∂q˙j)arrow_forwardProblem #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]arrow_forwardThis problem is designed to give you practice using the Dirac delta function. Eval- uate the following integrals. Show your reasoning.arrow_forward
- Problem 9.4 For the 2D LHO with K1 = K2 show that and [ê, ²] = 2ihxy, (ê, p}] = -2ihxy Problem 9.5 It follows from the above that [ê., Ĥ] = 0 if K1 = K2 only Work out the equivalent commutator for ê and é, with the Hamiltonian. What do these mean?arrow_forwardA potential Vo(0) = k sin² (0/2) (k is a constant) is present on the surface of a hollow sphere ofradius R.1. Find the potential Vout(r, 0) outside the sphere (i.c., for r > R).arrow_forwardProblem 10.10 Consider a central force given by F(r) = -K/r³ with K > 0. Plot the effective potential and discuss possible types of motion.arrow_forward
- Question 6: The dispersion relation of a system is given by w(k) = 2w, sin, where wo is a constant and n is an integer. 1. Calculate the group velocity vg. 2. Calculate the phase velocity Uph.arrow_forwardProblem 4.12 Calculate the potential of a uniformly polarized sphere (Ex. 4.2) directly from Eq. 4.9.arrow_forwardA point particle moves in space under the influence of a force derivablefrom a generalized potential of the formU(r, v) = V (r) + σ · L,where r is the radius vector from a fixed point, L is the angular momentumabout that point, and σ is the fixed vector in space. Find the components of the force on the particle in Cartesian coordinates, on the basis of the equation for the components of the generalized force Qj: Qj = −∂U/∂qj + d/dt (∂U/∂q˙j)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning