Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 42E
To determine

To Rewrite:The given equation as L^2θΦ=C2θΦ

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In spherical polar coordinates, the angular momentum operators, 1² and Îz, can be written, Ә β = -ħ² 1 ə sin Ꮎ ᎧᎾ 1 2² sin² 0 00² дф él sin)+ + and (a) îψ(θ, φ) = λιψ(θ, φ) = Î₂ = = -ih Apply these operators to the unnormalized eigenfunction, (0, 4) = sin²0 e-²ip, and determine the eigenvalues of that are associated with each operator. (b) Î₂¥(0, 0) = 1₂4(0,4)
QUESTION 3: Abstract angular momentum operators: In this problem you may assume t commutation relations between the general angular momentum operators Ĵ, Ĵy, Ĵz. Use whenev possible the orthonormality of normalised angular momentum eigenstate |j, m) and that α = Îx±iĴy, Ĵ²|j,m) = ħ²j(j + 1)|j,m) and Ĵz|j,m) (a) Express ĴĴ_ in terms of Ĵ² and Ĵ₂. = ħmlj, m). (b) Using the result from (a) find the expectation value (j,m|εÎ_|j,m). (This is the nor squared of the state Î_|j,m).)
Consider the Laplace's equation u t uyy = 0 in the square 00 find the associated eigenfunctions X,(x) forn= 1,2,3, - c) Using the boundary condition calculate Y, y) d) Calculate the coefficients (c,) to satisfy the nonhomogeneous condition e) Write a formal series solution of the problem.

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