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Solution of Schrodingers Equation for the Kepler Problem

Solution of Schrodinger s Equation for the Kepler Problem [Pg.298]

Changing to three-dimensional polar co-ordinates r, 0, cf), we obtain the equation [Pg.298]

The second equation is the equation defining the spherical harmonic Pf GOs0), when A has the value 1) and m Z for other values the equation has no finite one-valued solution. We shall prove this generally by combining the 6 and -relationships in the general surface harmonic Yi 9, cf)). If for brevity we introduce the notation [Pg.299]

A general solution of this equation is obtained in the following way. We consider a homogeneous polynomial Ui of the Z-th degree in x, y, z, which satisfies Laplace s equation [Pg.299]

It is possible to prov( . tliat no other vaf iu s of Agiv( - finite and continuous one-valued solutions of the diifer( ntial ( quation. The ])r op(U values of the equation AY.+AF,= 0 [Pg.299]




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Kepler

Kepler problem

Keplerates

Schrodinger equation solutions

Schrodinger solutions

Solution of equations

Solution of the Schrodinger equation

Solution of the problem

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