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 10.3, Problem 10.7P
To determine
Obtain the partial wave phase shift for S-wave due to the scattering from a delta function shell given in problem 10.4.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Normalize the wave function Ψ (x) = A exp (–ax2), A and a are constants, over the domain −∞ ≤ x ≤ ∞
According to Ehrenfest's theorem, the time evolution of an expectation value <A>(t) follows the Ehrenfest equations of motion (d/dt)<A>(t) = (i/[hbar])<[H,A]>(t).
For the harmonic oscillator, the Hamiltonian is given by H = p2/2m + m[omega]2x2/2.
a) Determine the Ehrenfest equations of motion for <x> and <p>.
b) Solve these equations for the initial conditions <x> = x0, <p> = p0, where x0 and p0 are real constants.
Better formatted version of the question attached.
Find the Dual of the function below and check if it is self-dual:F4 = (XY + YZ + ZX)
Knowledge Booster
Similar questions
- The 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_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_forwardAt what displacements is the probability density a maximum for a state of a harmonic oscillator with v = 1? (Express your answers in terms of the coordinate y.)arrow_forward
- Calculate the period of oscillation of ?(x,t) for a particle of mass 1.67 × 10-27 kg in the first excited state of a box of width 1.68 × 10-15 m. Include a sketch of U(x) and ?(x).arrow_forwardAn anharmonic oscillator has the potential function V = 1/2.(k.x^2) + c.x^4 where c can be considered a sort of anharmonicity constant.Determine the energy correction to the ground state of theanharmonic oscillator in terms of c, assuming that H^° is theideal harmonic oscillator Hamiltonian operator.arrow_forwardWhat does your result for the potential energy U(x=+L) become in the limit a→0?arrow_forward
- Locate the nodes of the harmonic oscillator wavefunction with v = 3.arrow_forwardShow that the uncertainty in the momentum of a ground-state harmonic oscillator is (where h is h-bar, m is the mass, and k is the spring constant).arrow_forwardA definite-momentum wavefunction can be expressed by the formula W(x) = A (cos kx +i sin kx), where A and k are constants. Show that, if a particle has such a wavefunction, you are equally likely to find it at any position x.arrow_forward
- Two mass points of mass m1 and m2 are connected by a string passing through a hole in a smooth table so that m1 rests on the table surface and m2 hangs suspended. Assuming m2 moves only in a vertical line, what are the generalized coordinates for the system? Write the Lagrange equations for for the system and, if possible, discuss the physical significance any of them might have. Reduce the problem to a single second-order differential equation and obtain a first integral of the equation. What is its physical significance? (Consider the motion only until m1 reaches the hole.)arrow_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_forwardLet f(x)= 4xex - sin(5x). Find the third derivative of this function. Note ex is denoted as e^x below. Select one: (12+4x^3)e^x + 125sin(5x) 12e^x + 125cos(5x) not in the list (12+4x)e^x + 125cos(5x) (8+4x)e^x + 25sin(5x)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
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher: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
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax