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

Boundary Conditions for Hydrogen Schrodinger Equation

  1. Jan 23, 2015 #1
    If I am trying to derive the energy eigenvalues and quantum numbers for the hydrogen atom (basic hydrogen-1), I obviously need to solve the hydrogen Schrodinger equation and account for some boundary conditions. However, no website ever gives me the boundary conditions. What would be the boundary conditions for the hydrogen atom?
     
  2. jcsd
  3. Jan 23, 2015 #2

    DEvens

    User Avatar
    Education Advisor
    Gold Member

    The usual thing is to have the wave function go to zero as radius goes to infinity. Is that enough?
     
  4. Jan 23, 2015 #3

    Quantum Defect

    User Avatar
    Homework Helper
    Gold Member

    Integral of Psi*Psi needs to be finite (square integrable). You can have a function go to zero as r->inf. that would not be square integrable.
     
  5. Jan 23, 2015 #4
    The usual method of separation of variables imposes a 'boundary' condition that the spatial components of the solution are independent of time - i.e. time-invariant.
    This may be excessive, as the requirement that the final wave function be square-integrable permits wave functions that are periodic with finite integrability.
    The other boundary conditions also imposed by the method are that the components of the wave function in polar coordinates are orthogonal and normal.
    The polar coordinates themselves are part of this, in that in other coordinate systems (rectilinear, cylindrical) the wave functions are NOTsquare-integrable.
     
  6. Jan 23, 2015 #5

    DEvens

    User Avatar
    Education Advisor
    Gold Member

    That is normalization, not boundary condition.
     
  7. Jan 24, 2015 #6

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    And you can have square integrable functions which don't go to 0 when their argument goes to infinity.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook