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 8.1, Problem 8.3P
To determine
The best bound on
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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)
Consider the Lennard-Jones potential between atoms in a solid material.
Find the dependence of the equilibrium postion x0, on the parameters in the potential. Then for small perturbations, δx around x0, determine the restoring force as a function of δx.
What does your result for the potential energy U(x=+L) become in the limit a→0?
Chapter 8 Solutions
Introduction To Quantum Mechanics
Knowledge Booster
Similar questions
- Verify that each of the following force fields is conservative. Then find, for each, a scalar potential φ such that F = −∇φ.(1). F = i − zj − yk.arrow_forwardShow that the total energy eigenfunctions ψ210(r, θ, φ) and ψ211(r, θ, φ) are orthogonal. Doyou have to integrate over all three variables to show this?arrow_forwardThe Brachistochrone Problem: Show that if the particle is projected withan initial kinetic energy 1/2 m v02 that the brachistochrone is still a cycloidpassing through the two points with a cusp at a height z above the initialpoint given by v02 = 2gz.arrow_forward
- Find the Dual of the function below and check if it is self-dual:F4 = (XY + YZ + ZX)arrow_forwardA (nonconstant) harmonic function takes its maximum value and its minimum value on the boundary of any region (not at an interior point). Thus, for example, the electrostatic potential V in a region containing no free charge takes on its largest and smallest values on the boundary of the region; similarly, the temperature T of a body containing no sources of heat takes its largest and smallest values on the surface of the body. Prove this fact (for two-dimensional regions) as follows: Suppose that it is claimed that u(x, y) takes its maximum value at some interior point a; this means that, at all points of some small disk about a, the values of u(x, y) are nolarger than at a. Show by Problem 36 that such a claim leads to a contradiction (unless u = const.). Similarly prove that u(x, y) cannot take its minimum value at an interior point.arrow_forwardThe wavefunction of is Ψ(x) = Axe(−ax^2)/2 for with energy E = 3aℏ2/2m. Find the bounding potential V(x). Looking at the potential’s form, can you write down the two energy levels that are immediately above E?arrow_forward
- Use the fact that at the critical point the first and second partial derivatives of P with respect to Vm at constant T are zero (∂P/∂Vm=∂2P/∂V2m=0) to derive the expressions for the Van der Waals constants in terms of critical parameters. Show full and complete procedure, do not skip any steparrow_forwardThe wavefunction of is Ψ(x) = Axe−αx2/2 for with energy E = 3αℏ2/2m. Find the bounding potential V(x). Looking at the potential’s form, can you write down the two energy levels that are immediately above ??arrow_forwardfind a potential function for F or determine that F is not conservative. F = xj + ykarrow_forward
- Find the wave function and energy for the infinite-walled well problemCould you explain it to me step by step and in detail?Thanks a lotarrow_forwardIn class, we developed the one-dimensional particle-in-a-box model and showed that the wavefunction Ψ(x) = Asin(kx), where k = nπ/l, where n is a positive integer and l is the length of the box: (a) by normalizing the wavefunction, determine the constant A; (b) by applying the Hamiltonian, determine the expression for energy as a function of n and l.arrow_forwardThe Hamiltonian of a spin in a constant magnetic field B aligned with the y axis is given by H = aSy, where a is a constant. a) Use the energies and eigenstates for this case to determine the time evolution psi(t) of the state with initial condition psi(0) = (1/root(2))*matrix(1,1). (Vertical matrix, 2x1!) b) For your solution from part (a), calculate the expectation values <Sx>, <Sy>, <Sz> as a function of time. I have attached the image of the orginial question!arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax