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Metamusing (talk | contribs) m →Reference frame in classical mechanics and inertial frame: removed redundancy |
m Fixed minus sign in the Schrodinger equation and a minus sign in front of the kinetic energy operators in the following equation. |
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Now consider the Schrödinger equation for the proton and the electron:
:::<math>\frac{\partial}{\partial t}\Psi(x_1,y_1,z_1,x_2,y_2,z_2,t)=-iH\Psi(x_1,y_1,z_1,x_2,y_2,z_2,t)</math>
A change of variables to relational and centre-of-mass coordinates yields
:::<math>\frac{\partial \Psi(x,y,z,X,Y,Z)}{\partial t} = -i[-\frac{1}{2M}\nabla_{c.o.m.}^2
where <math>M</math> is the total mass and <math>\mu</math> is the reduced mass. A final change to spherical coordinates followed by a separation of variables will yield the equation for <math>\Phi(r,\theta,\phi)</math> from above.
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