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Show that E1-E0 is constant.(changing potential of Schrodinger's eq)

  1. Jul 23, 2011 #1
    1. The problem statement, all variables and given/known data

    If potential of Schrodinger's eq(1-D) is ln(x)(log(x)), show that E1-E0(E0 is ground E)

    is just constant.(x>0)

    2. Relevant equations

    This problem is a supplement problem of chapter 4 in

    Quantum Mechanics: An Accessible Introduction.(Robert Scherrer)

    3. The attempt at a solution

    I want to get simple solution, not complex calculation.(using Frobenius theorem)

    So I assume plot of potential ln(x) can be approximate to hydrogen potential problem.

    (if x is very small)

    (Energy value of hydrogen is just E=k/n^2)

    But I think this approximation is not correct.

    How should I do to get solution?

    And this problem is really needed tough calculation method?
  2. jcsd
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