How do we differenciate between theoretical-physics and mathematical-physics? Mathematical-physics is an area of mathematics. Then problems related to it should be posted on Math.SE. If it is related to how a physical concept is related/comming from the mathematical theory then should be in Physics.SE.
Questions that are related with physics are welcome in Math.SE. They have tags like physics, quantum-mechanics, mathematical-physics, classical-mechanics, etc. usually for solving mathematical problems that arise when we are dealing with physics questions. These type's of questions will not be welcome in Physics.SE. The Physics.SE community is more reluctant to answer questions that deals only with mathematics of problems, or in how you approach your homework or in general calculations in some result.
If you want to ask a question here you should see the policy of how to ask a question. If it deals with concepts of physics the question is off-topic and should migrate or be deleted. If the question is asking about the mathematics part of the theory it may be well received.
Is this question in mathematical-physics? Yes. Your question deals with mathematical-physics. If you look standard mathematical physics textbooks will treat these kind of method to solve partial differential equations. There are several equations that are solved using these treatments in physics. To me your tags are correct. The problem is in the text. It is important to set correctly the functions, say what are the domains and etc, say what are all the equations (mathematical experts in partial differential equations do not need to know the time-independent Schroedinger equations), say what are all the constants and what type of function is $V$. This is very important for mathematical-physics and mathematicians, and is something that usually physics don't care a lot.
What is mathematical-physics? With modern knowledge, mathematical-physics is an area of research within the theoretical physics and mathematics, that is characterized not by studying specific physical systems, like the areas of Mechanics of Thermodynamics, but by presenting a specific approach when dealing with physical problems. More specifically, Mathematical-Physics deals primarily with mathematical rigor and clearness in theoretical physics, trying to enrich concepts and set rigor in the mathematics used by physicists.