Boundary problem with parameter using NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg93290] Boundary problem with parameter using NDSolve*From*: Mikhail Lemeshko <mikhail.lemeshko at gmail.com>*Date*: Mon, 3 Nov 2008 05:25:00 -0500 (EST)

Dear friends, I hope you can help me with the following problem. I try to solve the Schr=F6dinger equation for some arbitrary potential V(x): -f''[x] + V[x]*f[x] == ee*f[x] Considering discrete energy levels (ee<0), there are also boundary conditions f[0]==f[some_very_big_x]==0, which are satisfied only at some values of the parameter ee. I wish to find the values of energy ee and the corresponding wavefunctions. Is there an easy method to do it with Mathematica? I mean, to write a code "here are the equations with boundary conditions, please find all values of ee in the interval from E1 to E2, where the boundary conditions are satisfied, and return me the list of them"? Or, I have to implement a cycle, which will increase the energy step- by-step and check whether the boundary conditions are satisfied? Thank you a lot in advance, Mikhail.