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Published byVanessa Frazier Modified over 2 years ago

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1 L10 – QM in 3 dimensions

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2 V(r): separation of variables

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4 The angular equation

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5 The angular equation -

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6 P l are the Legendre polynomials, defined by the Rodrigues formula:

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9 Spherical harmonics = (-1) m for m>=0 and =1 for m<0. The Y are orthogonal, so

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10 The radial equation

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11 L11 – The H atom u(r) = rR(r)

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12 Asymptotic behavior u(r) = rR(r)

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13 The radial solution u(r) = rR(r) n > l is the q-th Laguerre polynomial.

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14 The radial solution: energy

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15 Ground state

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16 n > 1

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17 n > 1 (continued) Since they are eigenvectors for different eigenvalues

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18 Example

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19 Graphs

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20 Angular momentum Poiche Poiche, lequazione in si puo scrivere

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