Answer the following about an observable that is represented by the operator Â = wo (3² + 3²). ħ (4) Is it possible to write a complete set of basis states that are simultaneously eigenstates of the operator Ĵ and Â? If so, explain how you know. If not, write an uncertainty principle for the observables A and J.

Answer the following about an observable that is represented by the operator Â = wo (3² + 3²). ħ (4) Is it possible to write a complete set of basis states that are simultaneously eigenstates of the operator Ĵ and Â? If so, explain how you know. If not, write an uncertainty principle for the observables A and J.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

PROBLEM 2 Calculate the probability distribution of momenta p for a ld oscillator in the ground state (n = 0). Calculate the mean square dispersions (x2), (p²), and the product (r2)(p²).
What’s Orthogonal Set in quantum mechanics? And Write its mathematical formula
The Hamiltonian for the one dimensional quantum oscillator is 1 p² 1 Ĥ = 1² + ½ k²² = 12 + √ mw² à² 2m 2m 2 where k = mw². 1) Define the operators ₁₁ and ₁₁ such that Ĥ = ½ħw (p² + ²). Define Ĥ2 as a function of 1 and p₁ such that Ĥ = hwĤ₂. - 2) Let us define the new operators â (1 + i₁) and â† = ½(î₁ — ip₁). Express ₁ and p₁ as a function of â and â³. Knowing that [^^1,î₁] = i and [1, 1] = -i, calculate âât and â†â. Express Ĥ2 as a function of a and at. 3) Let us define Ñ such that Ĥ₂ = Ñ + ½. Knowing that Ĥ, Ĥ₂ and Ñ have the same eigenstates, what are their corresponding eigenvalues?
The Hamiltonian of an electron of mass m in a constant electric field E in one dimension can be written as Ĥ=+eEx where â and are the position and momentum operators, respectively. With initials conditions (t = 0) = 0 and p(t = 0) = 0, which one of the following gives (t) at time in the Heisenberg picture? You may use the commutator [â,p] = iħ. O a. O b. eEt2 2m O C. e Et O d. -eEt O e. eEt² m pt m
O Consider the kinetic energy matrix elements between Hydrogen states (n' = 4, l', m'| |P|²| m -|n = 3, l, m), = for all the allowed l', m', l, m values. What kind of operator is the the kinetic energy (scalar or vector)? Use this to determine the following. For what choices of the four quantum numbers (l', m', l, m) can the matrix elements be nonzero (e.g. (l', m', l, m) (0, 0, 0, 0),...)? Which of these nonzero values can be related to each other (i.e. if you knew one of them, you could predict the other)? In this sense, how many independent nonzero matrix elements are there? (Note: there is no need to calculate any of these matrix elements.)
please provide detailed solutions for a to d. thank you!