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Hydrogenic Atoms

  • Julian Schwinger
Chapter

Abstract

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
$$\left[ {\frac{{{d^2}}}{{d{\rho ^2}}} - \frac{{{m^2} - \frac{1}{4}}}{{{\rho ^2}}} + 2\left| m \right| + {n_\rho } + 2 - {\rho ^2}} \right]u(\rho ) = 0$$
(8.1.1)
, and put
$${p^2} = 2\lambda r\quad with\quad \lambda > 0$$
(8.1.2)
.

Keywords

Hydrogenic Atom Energy Eigenvalue Hamilton Operator Virial Theorem Homogeneous Magnetic Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Julian Schwinger

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