Landau's nonrelativistic quantum mechanics has a "derivation" of Schroedinger's equation using what he calls "the variational principle". Apparently such a principle implies that:(adsbygoogle = window.adsbygoogle || []).push({});

$$\delta \int \psi^{\ast} (\hat{H} - E) \psi dq = 0$$

From here I can see that varying ##\psi## and ##\psi^{\ast}## independently gives rise to the equation ##\hat{H} \psi = E \psi##. But where does that first equation come from? I think it is saying that the the allowed energies are those for which the difference between the expectation value of the hamiltonian and the energy is minimized. I'm not sure why that should be so. Is there some analogue to classical mechanics that I'm missing?

(Note: this is section 20 of the book).

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

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

# I Schroedinger Equation from Variational Principle

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Schroedinger Equation Variational | Date |
---|---|

B Schroedinger Equation and Hamiltonian | Jun 21, 2017 |

I The energy term in Schroedinger equation | May 12, 2016 |

Solution to Schroedinger Equation for a huge hypothetical | Feb 4, 2015 |

Schroedinger Equation | Oct 19, 2013 |

Analytic Solutions to Schroedinger Equation | Sep 25, 2013 |

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