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?