L14. H atom

L14. H atom - Schroedinger equation in spherical...

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Ψ ( r , θ , φ ) = Ε Ψ ( r , θ , φ ) Schroedinger equation in spherical coordinates Ψ ( r , θ , φ ) V(r)
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E n proportional to 1/n 2 E n n 2 n 2 n
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V(r) V(r) Use of spherical coordinates, separation of variables and some algebraic manipulations yield two separate equations for radial and angular part β β β = positive constant
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Separation of angular variables Equation for the rigid rotor β β
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Equation for the rigid rotor “split” into two separate equations β m 2 m 2 -m 2 -m 2
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Single valued function Equation for the rigid rotor “split” into two separate equations : SOLVE Eq. I -m 2 Quantization of m
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Equation for the rigid rotor “split” into two separate equations : SOLVE Eq. II m 2 β quantization of b
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We have solved the rigid rotor equation phase
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We have solved the rigid rotor equation
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Some Spherical Harmonics
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The Hamiltonian of the rigid rotor and the operator L 2 eigenvalues
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we have seen a couple of weeks ago that:
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Angular momentum components in spherical coordinates
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V(r) V(r) Use of spherical coordinates, separation of
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This note was uploaded on 01/21/2011 for the course ENG 167 taught by Professor Phillips during the Winter '07 term at UC Davis.

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L14. H atom - Schroedinger equation in spherical...

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