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In quantum mechanics the study of Schödinger equation for the hydrogen atoms leads to a con sideration of Laguerre's equation con- xy" + (1 – x)y/ + Ay = 0 , x > 0 where A is a parameter. Use the reduction of order to obtain a second linearly independent solution to Laguerre 's equation for the given value of A and the corresponding solution f(x) a)A = 1, f(r) = (1 – x) b)A = 2, f(x) = x² – 4.x + 2 Hint: e" =1+r+

In quantum mechanics the study of Schödinger equation for the hydrogen atoms leads to a con sideration of Laguerre's equation con- xy" + (1 – x)y/ + Ay = 0 , x > 0 where A is a parameter. Use the reduction of order to obtain a second linearly independent solution to Laguerre 's equation for the given value of A and the corresponding solution f(x) a)A = 1, f(r) = (1 – x) b)A = 2, f(x) = x² – 4.x + 2 Hint: e" =1+r+

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In quantum mechanics the study of Schödinger equation for the hydrogen atoms leads to a con- sideration of Laguerre's equation xy" + (1 – r)y/ + Ay = 0 , r > 0 where A is a parameter. Use the reduction of order to obtain a second linearly independent solution to Laguerre 's equation for the given value of A and the corresponding solution f(x) a)A = 1, f(x) = (1 – r) b)A = 2, f(x) = x² – 4x + 2 Hint: e z1+x +
Transcribed Image Text:In quantum mechanics the study of Schödinger equation for the hydrogen atoms leads to a con- sideration of Laguerre's equation xy" + (1 – r)y/ + Ay = 0 , r > 0 where A is a parameter. Use the reduction of order to obtain a second linearly independent solution to Laguerre 's equation for the given value of A and the corresponding solution f(x) a)A = 1, f(x) = (1 – r) b)A = 2, f(x) = x² – 4x + 2 Hint: e z1+x +
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