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Math Help - Quantum Mechanics

  1. #1
    Junior Member
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    Quantum Mechanics

    Hi, can someone let me know what kind of maths I need to learn to be able to understand and solve the Schrodinger Equation for a hydrogen atom?

    According to my textbook the Schrodinger Equation tells you the principal quantum number, the azimuthal quantum number and the magnetic quantum number, can someone let me know HOW these are derived from the solution?

    Lastly, can I determine the shapes of the s, p, d and f orbitals of a hydrogen atom by solving the Schrodinger Equation?

    (I posted this on the physics help forum but decided it has more to do with maths, how do I delete my other post?
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  2. #2
    Super Member Aryth's Avatar
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    The solution to the Hydrogen Schrodinger Equation is rigorous but is managed by separation of variables:

    \psi(r, \theta, \phi) = R(r)P(\theta)F(\phi)

    Where

    R(r) = n = \text{Principal Quantum Number}

    P(\theta) = l = \text{Orbital Quantum Number}

    F(\phi) = m_l = \text{Magnetic Quantum Number}

    The separation leads to three separate equations. Solving these spatial equations gives the three quantum numbers.

    Here's a picture:



    And here's a website:

    Hydrogen Schrodinger Equation

    I think this is what you're looking for.
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