# Changing the form of a second order DE to look like the Schrödinger equation

• February 17th 2010, 04:25 PM
robotENGR
Changing the form of a second order DE to look like the Schrödinger equation
I ran into a predicament... I have the following equation:

http://www.mathhelpforum.com/math-he...f27a9feb-1.gif

how can I convert it to a form that looks like:

http://www.mathhelpforum.com/math-he...2060f1f4-1.gif

or of the form:

http://www.mathhelpforum.com/math-he...d6983420-1.gif
• February 18th 2010, 05:58 AM
shawsend
You can convert $y''+Py'+Qy=0$ into its normal form $v''+Iv=0$ by letting $y=v\,\exp\left(-1/2\int Pdx\right)$

Got two references for you: "Intermediate Differential Equations" by Rainville and Handbook of Differential Equations by Zwillinger. Try and find them in the library.