How to eliminate the error FindRoot::lstol?

Questions
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1

The following notebook, aka, FixMQM2eFig2p5.nb is created by Jim Napolitano tuf43817@temple.edu for his Modern Quantum Mechanics (3rd edition).

When I try to run it, I meet the FindRoot::lstol message as shown below, and I want to know how to eliminate it.

Open in Wolfram Cloud ↗

Regards,
Zhao

2

Try:

  v = x^2 + x^4;
  pfun = ParametricNDSolveValue[{-u''[x] + v u[x] == \[Epsilon] u[x], 
      u[0] == 1, u'[0] == 0}, u, {x, -10, 10}, {\[Epsilon]}];
   \[Epsilon]Val1 = \[Epsilon] /. FindRoot[pfun[\[Epsilon]][9], {\[Epsilon], 40}, 
     Method -> "AffineCovariantNewton"]

 (*40.6904*)
3

Nice, it does the trick.