An electron (spin s = 1/2) in an = 1 state of orbital angular momentum can...

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An electron (spin s = 1/2) in an = 1 state of orbital angular momentum can be decom- posed by 10 = 2012. Let us find the first few coupled states |ls; JM) in terms of the uncoupled basis Ils; mems), using the ladder operators. 33 (a) Write down the highest M state, [11; 32), in terms of the uncoupled basis. 31 (b) Use the lowering operator to obtain the state [1;2). (c) Use orthogonality to obtain the state [11; 1¹). (One could continue using the lowering operator to obtain the remaining states, but we'll stop there.) (d) Check your answers by constructing the same three states using the Clebsch-Gordan coefficients in the attached table. An electron (spin s = 1/2) in an = 1 state of orbital angular momentum can be decom- posed by 10 = 2012. Let us find the first few coupled states |ls; JM) in terms of the uncoupled basis Ils; mems), using the ladder operators. 33 (a) Write down the highest M state, [11; 32), in terms of the uncoupled basis. 31 (b) Use the lowering operator to obtain the state [1;2). (c) Use orthogonality to obtain the state [11; 1¹). (One could continue using the lowering operator to obtain the remaining states, but we'll stop there.) (d) Check your answers by constructing the same three states using the Clebsch-Gordan coefficients in the attached table.

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a The highest M state for an electron with spin s12 in an 1 state of orbital angular momentum is JM3... View the full answer