Change of variables in QHO with constant electric field

[JJfortherear]

http://imgur.com/cbQ44

I'm just not sure how they come up with that...

*note, the E₀ is not ground state energy, it's a constant electric field.

 

[vela]

Look at it as two change of variables: one to make the equation dimensionless and one to get rid of the term linear in x.