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 3.3, Problem 3.8P
(a)
To determine
The eigen values of the Hermitian operator
(b)
To determine
The eigen values of the Hermitian operator
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Show 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?
Evaluate the commutator [Â,B̂] of the following operators.
For a one dimensional system, x is the position operator and p the momentum operator in the x direction.Show that the commutator [x, p] = ih
Chapter 3 Solutions
Introduction To Quantum Mechanics
Ch. 3.1 - Prob. 3.1PCh. 3.1 - Prob. 3.2PCh. 3.2 - Prob. 3.3PCh. 3.2 - Prob. 3.4PCh. 3.2 - Prob. 3.5PCh. 3.2 - Prob. 3.6PCh. 3.3 - Prob. 3.7PCh. 3.3 - Prob. 3.8PCh. 3.3 - Prob. 3.9PCh. 3.3 - Prob. 3.10P
Ch. 3.4 - Prob. 3.11PCh. 3.4 - Prob. 3.12PCh. 3.4 - Prob. 3.13PCh. 3.5 - Prob. 3.14PCh. 3.5 - Prob. 3.15PCh. 3.5 - Prob. 3.16PCh. 3.5 - Prob. 3.17PCh. 3.5 - Prob. 3.18PCh. 3.5 - Prob. 3.19PCh. 3.5 - Prob. 3.20PCh. 3.5 - Prob. 3.21PCh. 3.5 - Prob. 3.22PCh. 3.6 - Prob. 3.23PCh. 3.6 - Prob. 3.24PCh. 3.6 - Prob. 3.25PCh. 3.6 - Prob. 3.26PCh. 3.6 - Prob. 3.27PCh. 3.6 - Prob. 3.28PCh. 3.6 - Prob. 3.29PCh. 3.6 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Prob. 3.40PCh. 3 - Prob. 3.41PCh. 3 - Prob. 3.42PCh. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48P
Knowledge Booster
Similar questions
- Using the condition (3.027) of Lect. 16, prove that the mo- mentum operator p is Hermitian. HINT: Use the periodic boundary conditions for the functions g(r) and s(x).arrow_forwardShow that the operator H = -1/2(d^2/dx^2) is hermitian, assuming that it operates on a Hilbert space of L^2 functions whose functions and derivatives vanish at x = −∞ and x = +∞arrow_forwardShow that the function ψ = 8e5x is an eigenfunction of the operator d/dx. What is the eigenvalue? Prove that the momentum operator corresponding to px is a Hermitian operator. Show solutions please. thanks!arrow_forward
- Calculate the hermitian conjugate (adjoins) for operator d/dxarrow_forwardThe energy of the Hamiltonian operator defined below for the one-dimensional anharmonic oscillator Calculate first-order contributions to eigenvalues. (Here ? is a small number.)arrow_forwardshow hamiltonian operator for the plane waves (exponential, imaginary) Prove that this operator does not change this function. Prove that this operator does generate energy of a particle in free space.arrow_forward
- Obtain the value of the Lagrange multiplier for the particle above the bowl given by x^2+y^2=azarrow_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 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_forwardTwo 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_forward
- In 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_forwardWhat does your result for the potential energy U(x=+L) become in the limit a→0?arrow_forwardDemonstrate that in an electromagnetic field, the gauge transformation transfers the L to an equivalent Lagrangian L', where L' = L+ dFG,1 and F(q, t) is a function of generalised coordinates (q:) and time t. Calculate the generalised momentum and Hamiltonian of the charged particle travelling in an electromagnetic field using the aforementioned Lagrangian.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 LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
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