p41_013 - m ` is zero, so the largest q L 2 x + L 2 y can...

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13. Since L 2 = L 2 x + L 2 y + L 2 z , q L 2 x + L 2 y = p L 2 L 2 z . Replacing L 2 with ` ( ` +1)¯ h 2 and L z with m ` ¯ h ,we obtain q L 2 x + L 2 y h q ` ( ` +1) m 2 ` . For a given value of ` , the greatest that m ` can be is ` , so the smallest that q L 2 x + L 2 y can be is ¯ h p ` ( ` +1) ` 2 h ` . The smallest possible magnitude of
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Unformatted text preview: m ` is zero, so the largest q L 2 x + L 2 y can be is h p ` ( ` + 1). Thus, h ` q L 2 x + L 2 y h p ` ( ` + 1) ....
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