Hydrogenic Atoms

  • Julian Schwinger


Now we are going to do a nice little trick: turn one kind of dynamical system into another one. Begin with the differential equation (7.4.60) that determines the energy eigenstates of the two-dimensional isotropic oscillator
$$\left[ {\frac{{{d^2}}}{{d{\rho ^2}}} - \frac{{{m^2} - \frac{1}{4}}}{{{\rho ^2}}} + 2\left| m \right| + {n_\rho } + 2 - {\rho ^2}} \right]u(\rho ) = 0$$
, and put
$${p^2} = 2\lambda r\quad with\quad \lambda > 0$$


Hydrogenic Atom Energy Eigenvalue Hamilton Operator Virial Theorem Homogeneous Magnetic Field 
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© Springer-Verlag Berlin Heidelberg 2001

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  • Julian Schwinger

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