All Questions
4
questions
0
votes
1
answer
34
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Spectrum of a positive definite differential operator
When solving the two body problem in three dimensions in my QM lectures, you end up, essentially, with the Legendre associated equation. In terms of the angular momentum operator:
$$L^2Y_l^m(\theta, \...
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1
vote
1
answer
49
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Fundamental property of Green's function is violated
$$\langle x| D|x'\rangle=D_x\langle x|x'\rangle=D_x\,\delta(x-x')$$
$DD^{-1} = I$ , Where '$I$ ' represents the Identity
position representation of this equation is
$\langle x|D|x'\rangle \langle ...
- 39
1
vote
0
answers
94
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How boundary conditions for a green function is same a original function
I am trying to study green's function.suppose we have a differential equation,
$D_x f(x) =g(x)$ , We also provided with some boundary conditions for $f(x)$, But we supply this boundary conditions in ...
- 39
6
votes
1
answer
985
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Kernel of adjoint operator
This problem is puzzling me, even though it should be really simple.
Let $L=-\partial_x^2 + \frac 1 2 x^{-2}$ be an operator defined on $D(L)=C^\infty_c(0,+\infty)\subset L^2(0,+\infty)$. Its adjoint ...
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