Apply these operators to the unnormalized eigenfunction, (0, ¢) = sin² 0 e-²i, and determine the eigenvalues of that are associated with each operator.

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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)
Transcribed Image Text: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)
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