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Hi,
I have done most of the problem in this word document (attached). I have some trouble though. In my QM class, we assumed that the z component of angular momentum Lz satisfies, Lz Ylm = m hbar Ylm and the ladder operator L+ and L were defined as L+_ = Lx + iLy. We were able to find the eigen values of Lx and Ly using the ladder operators.
In this problem initially they define Lx to satisfy Lx Ylm = m hbar Ylm and the continue to say tha Lx = 1/2 (L+ + L). How is this possible? Further, in part C, they are asking to find the eigen values of Lz. I am not sure how to find this. I would like to know what is Lz in terms of L+ and L. Please help me out if possible. Thank You,
Gamma
I have done most of the problem in this word document (attached). I have some trouble though. In my QM class, we assumed that the z component of angular momentum Lz satisfies, Lz Ylm = m hbar Ylm and the ladder operator L+ and L were defined as L+_ = Lx + iLy. We were able to find the eigen values of Lx and Ly using the ladder operators.
In this problem initially they define Lx to satisfy Lx Ylm = m hbar Ylm and the continue to say tha Lx = 1/2 (L+ + L). How is this possible? Further, in part C, they are asking to find the eigen values of Lz. I am not sure how to find this. I would like to know what is Lz in terms of L+ and L. Please help me out if possible. Thank You,
Gamma
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