Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A What are typical initial conditions for the Schrödinger eq?

  1. Dec 29, 2017 #1

    SeM

    User Avatar

    Hi, I am wondering if there exists some general initial conditions for solving the Schödinger eqn. for 1D free electrons ?

    Thanks!
     
  2. jcsd
  3. Dec 29, 2017 #2

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    Typically, in solving Schrodinger's equation, you are either doing a time-dependent analysis, in which case the initial conditions are part of the problem statement, or you are doing a time-independent analysis, in which case, people are usually looking for energy eigenstates.

    If you are doing a time-dependent analysis, the initial condition might be that the electron is a wave-packet of some sort localized at some particular position and momentum.
     
  4. Dec 29, 2017 #3

    SeM

    User Avatar


    Hi, I am doing a time-independent analysis, and thought of using the zero-point energy for E, in the Schrödinger eqn, and then solve it with the two initial conditions:

    1) assume that the wavefunction is 1 at position zero (x=0), as it would be normalized to.

    2) its slope, Psi', is zero at the same point, x=0. Does this sound reasonable?

    Thanks
     
  5. Dec 29, 2017 #4

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    If you already know a complete set of energy eigenstates then you can find a solution having those properties. Those properties don't help you find the eigenstates, though.
     
  6. Jan 2, 2018 #5

    SeM

    User Avatar


    I know, there is another procedure to find the eigenstates. This is just to find the analytical solution to the ground state.
     
  7. Jan 2, 2018 #6

    stevendaryl

    User Avatar
    Staff Emeritus
    Science Advisor

    I'm not sure what you mean. The ground is the eigenstate with the lowest energy. So if you know the eigenstates, you already know the ground state.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted