MathematicalPhysicist

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[tex](\frac{d^2}{dx^2}-k^2)\psi(x)=f(x)[/tex]

s.t it equals zero when x approaches plus and minus ifinity.

Now according to my lecturer I first need to solve the homogenoues equation, i.e

its solution is: psi(x)=Ae^(kx)+Be^(-kx)

and [tex]G(x,x')=\sum u_n^*(x)u_n(x)/(\lambda_n-\lambda)[/tex]

so u_n(x)=Ae^(xk_n)+Be^(-xk_n)

so as x approaches inifnity we get that A should be equal zero for green function to be zero, for x approaching minus infinity B should equal zero, so evetaully we get that G is identically zero, or am I missing something crucial, here?

how do i find the nth-eigenvalue of the eigenfunction u_n?