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In spherical polar coordinates, the angular momentum operators, L and Lz, can be written, a2 1 L2 = -h? 1 Îz = -ih- дф and |sin ở 36 (sin e) + sin² 0 a¤² sin 0 a0 Apply these operators to the unnormalized eigenfunction, (0, ¢) = sin? 0 e2i4, and determine the eigenvalues that are associated with each operator. (a) β(sin? 0 e2iø) = 1, (sin² 0 e2i¢) (b) Ê„(sin² 0 e2i¢) = 12(sin? 0 e2io)

In spherical polar coordinates, the angular momentum operators, L and Lz, can be written, a2 1 L2 = -h? 1 Îz = -ih- дф and |sin ở 36 (sin e) + sin² 0 a¤² sin 0 a0 Apply these operators to the unnormalized eigenfunction, (0, ¢) = sin? 0 e2i4, and determine the eigenvalues that are associated with each operator. (a) β(sin? 0 e2iø) = 1, (sin² 0 e2i¢) (b) Ê„(sin² 0 e2i¢) = 12(sin? 0 e2io)

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3. In spherical polar coordinates, the angular momentum operators, L and Lz, can be written, 1 L? = -h? 1 sin 0 ae) Îz = -ih and sin 0 a0 sin? 0 ap²] Apply these operators to the unnormalized eigenfunction, y(0,$) = sin² 0 e2i¢, and determine the eigenvalues that are associated with each operator. (a) L²(sin² 0 e2i¢) = 1, (sin² 0 e2io) (b) L„(sin² 0 e2io) = 12(sin² 0 e2iº)
Transcribed Image Text:3. In spherical polar coordinates, the angular momentum operators, L and Lz, can be written, 1 L? = -h? 1 sin 0 ae) Îz = -ih and sin 0 a0 sin? 0 ap²] Apply these operators to the unnormalized eigenfunction, y(0,$) = sin² 0 e2i¢, and determine the eigenvalues that are associated with each operator. (a) L²(sin² 0 e2i¢) = 1, (sin² 0 e2io) (b) L„(sin² 0 e2io) = 12(sin² 0 e2iº)
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