n********s
发帖数: 150 | 1 if f(x)=exp(ix), and there is an operator -i(d/dx), where x is angle,
then the eigenvalue of the operator should be 0,1,2,3.........
is it correct?
Why or why not?
Thanks a lot. | e**********n
发帖数: 359 | 2 You need to identify the Hilbert space (of the wavefunctions) first, which
is all periodic functions with period 2pi in this case. The operator -i(d/dx
) is an operator defined on this Hilbert space. Its eigenvalues are all
integers and the eigenfunctions are exp(i nx) with n \in Z. | g*****g
发帖数: 18 | 3 -i(d/dx)f(x)=Af(x), A is eigenvalue
thus f(x)=exp(iAx),
since x is angle
exp(iAx) should no difference with exp(iA(x+2pi))
therefore, exp(i2piA)=1, then A should be 0, 1, 2,...
-1, -2,....
( I am not sure it is right.) | n********s
发帖数: 150 | 4 I think you are right, thanks a lot, guys.
【在 n********s 的大作中提到】
: if f(x)=exp(ix), and there is an operator -i(d/dx), where x is angle,
: then the eigenvalue of the operator should be 0,1,2,3.........
: is it correct?
: Why or why not?
: Thanks a lot.
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