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 11.5, Problem 11.18P
(a)
To determine
The density matrix for an electron that is either in the state spin up along x or in the spin down along y.
(b)
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
What does your result for the potential energy U(x=+L) become in the limit a→0?
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?
Consider a classical of freedom" that is linear rather than quadratic: E = clql for some constant c. (An example would be the kinetic energy of a highly relativistic particle in one dimension, written in terms of its momentum.) Repeat the derivation of the equipartition theorem for this system, and show that the average energy is E= kT.
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
- At 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_forwardPlease add explanation and check answer properly before submit For a particle subjected to a harmonic oscillator potential, obtain the probability that the particle is outside the classical region, if it is in the ground state.arrow_forwardI have been able to do this with derivatives but I can't figure out how to do this with definite integralsarrow_forward
- The 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_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_forwardA free electron has a kinetic energy 13.3eV and is incident on a potential energy barrier of U =32.1eV and width w =0.091nm. What is the probability for the electron to penetrate this barrier (in %)? Check the correct answer and show all workarrow_forward
- For a particle in a box of length L sketch the wavefunction corresponding to the state with the lowest energy and on the same graph sketch the corresponding probability density. Without evaluating any integrals, explain why the expectation value of x is equal to L/2.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_forwardIf we have two operators A and B possess the same common Eigen function, then prove that the two operators commute with each otherarrow_forward
- A 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_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_forwardCalculate the expectation value of x2 in the state described by ψ = e -bx, where b is a ħ constant. In this system x ranges from 0 to ∞.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