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Question: Bounded solution of ODE

Question:Bounded solution of ODE

Zeineb 530 Maple
ode parameter dsolve bound
April 26 2016
0

Dear all

I have the following equaion

Eq := diff(phi(x, k), x, x)+(k^2+2*sech(x))*phi(x, k) = 0;
          
The solution is given by 

phi := (I*k-tanh(x))*exp(I*k*x)/(I*k-1);

My question : At what value of k is there a bound state and in this case can we give a simple form of the solution phi(x,k)

 

With best regards

 
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