Here's our equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d^2\psi}{du^2}+(\frac{\beta}{\alpha}-u^2)\psi=0[/tex]

This is the SE for the simple harmonic oscillator. My text goes through an elaborate solution to this DE and ends up resorting to a power series solution, not for psi, but for H, where [tex]\psi=H(u)e^{-u^2/2}[/tex]. The text also points out that no power series solution could be found by directly substituting in the SE for psi. However, Apostols THM6.13 (Volume II) states that any 2nd order ODE with analytic coefficients has a power series solution. Which is right?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Power Series Solution (SE)?

Loading...

Similar Threads for Power Series Solution | Date |
---|---|

Power series solution, differential equation question | Nov 12, 2015 |

Seek power series solutions of the given differential equation | Aug 31, 2015 |

Nonhomogeneous Power Series Solution | Mar 15, 2012 |

Factorial question in a power series solution | Oct 30, 2011 |

Power series solutions for ODEs. When are there how many of them? | Apr 2, 2011 |

**Physics Forums - The Fusion of Science and Community**