# Prove Sturm-Liouville differential operator is self adjoint.

#### shreddinglicks

Member warned that some effort must be shown on homework questions
1. The problem statement, all variables and given/known data
Prove Sturm-Liouville differential operator is self adjoint when subjected to Dirichlet, Neumann, or mixed boundary conditions.

2. Relevant equations
l = -(d/dx)[p(x)(d/dx)] + q(x)

3. The attempt at a solution
I have no idea. If someone can give me a place to start that would be awesome.

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#### LCKurtz

Homework Helper
Gold Member
1. The problem statement, all variables and given/known data
Prove Sturm-Liouville differential operator is self adjoint when subjected to Dirichlet, Neumann, or mixed boundary conditions.

2. Relevant equations
l = -(d/dx)[p(x)(d/dx)] + q(x)

3. The attempt at a solution
I have no idea. If someone can give me a place to start that would be awesome.
I haven't looked at that stuff for years, but my first suggestion to you is to give a more complete statement of the problem. By stating clearly what the problem is, you may see a way to solve it. For example, in the relevant equations you should list the various boundary conditions. Also give the definition of what it means for this differential operator to be self-adjoint. That will surely involve an integral or two. In other words, write down exactly what you need to prove. Once you carefully do that, if my memory serves me correctly, an integration by parts and using the BC's may solve your problem.

#### shreddinglicks

I haven't looked at that stuff for years, but my first suggestion to you is to give a more complete statement of the problem. By stating clearly what the problem is, you may see a way to solve it. For example, in the relevant equations you should list the various boundary conditions. Also give the definition of what it means for this differential operator to be self-adjoint. In other words, write down exactly what you need to prove. Once you carefully do that, if my memory serves me correctly, an integration by parts and using the BC's may solve your problem.
This is the complete statement of the problem that is on my homework sheet.

I looked over some examples I found through Google and came out with what is attached.

I'm gonna do some research into the boundary conditions later. I need a little break from studying.

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#### LCKurtz

Homework Helper
Gold Member
This is the complete statement of the problem that is on my homework sheet.
The homework helpers here don't have access to your class notes. You should post relevant definitions here.

I looked over some examples I found through Google and came out with what is attached.

I'm gonna do some research into the boundary conditions later. I need a little break from studying.
That looks like the sort of thing I was suggesting.

#### shreddinglicks

The homework helpers here don't have access to your class notes. You should post relevant definitions here.

That looks like the sort of thing I was suggesting.

I wish I had class notes, my teacher did not cover this and it's not in any textbook I have. If it seems I am on the right page then that's a relief.

"Prove Sturm-Liouville differential operator is self adjoint."

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