Quantum number and energy of electron



I computed the solution to Shroedinger's equation for an electron in
potential V(x) = mu x^4 and get that the electron energy is
Energy(qn):=7.0146168103584261*10^-21 * qn^1.341209441374369 -
6.3914598560847341*10^-21

for mu = 10^15

Curiously the exponent does not depend on mu (or hbar and m) and is
always 1.34120944137 to twelve places yet when I Google this number or the
first part of it I do not get any hits.  Am I missing something?

Rich