Applying an Operator to a Function: [(d^2/dx^2)-x^2]”

[eit32]

ok, i know that if we have operators A and B and a function f(x) that ABf(x) means that first B acts on f(x) and the A acts on the resulting function. But what it my operator looks like [(d^2 /dx^2) - x^2]. How do i apply this to my function. Do i just distribute my function to each part of the operator?

 

[G01]

Yes that is how you would apply that operator.

 

[eit32]

so [(d^2 /dx^2) - x^2]f(x) would just be (d^2 /dx^2)f(x) - x^2 f(x) ?

 

[G01]

Yes. That's correct.