If you've got, say, three particles, then the time-dependent Schrodinger equation (in units where [itex]\hbar = 1[/itex]) for the system reads(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

i \frac{\partial \psi}{\partial t} = -\sum_{i=1}^3 \frac{1}{2m_i} \Delta_i \psi + \sum_{i<j} V(r_i - r_j)\psi,

[/tex]

right? And of course [itex]\psi = \psi(r_1,r_2,r_3;t)[/itex]. But there isn't just ONE solution to this equation, right? There are MANY. And don't they correspond to, say, all particles being independent for large times, or one particle bound to another and the remaining one free, etc.? And I'm guessing this is at the heart of scattering theory - kind of examining the variety of long-time behaviors that can be exhibited in this case. Do I have this right?

**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!

# Time-dependent Schrodinger equation for many particles

Loading...

Similar Threads - dependent Schrodinger equation | Date |
---|---|

A Is my solution of time-dependent Schrodinger equation right? | Feb 4, 2017 |

Derivation of Time Dependent Schrodinger Equation | Jun 21, 2015 |

Schrödinger's time-dependent equation (general) | Dec 18, 2014 |

What is wavefunction in the time-dependent schrodinger equation? | Oct 31, 2013 |

Solutions to Time-dependent Schrodinger Equation | Aug 6, 2013 |

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