- #1
MathematicalPhysicist
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I need to find the green function of
[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?
[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?