Recent content by aop12

So I think I figured it out, but I would appreciate input on whether it is right or not. start with: eAeB = ex Then, looking for x x = log(eAeB) Which can be found using the Baker–Campbell–Hausdorff formula x = A + B + \frac{1}{2}[A,B] x = A + B + \frac{1}{2}C Thus, eAeB =...

Homework Statement Assume C=[A,B]≠0 and [C,A]=[C,B]=0 Show eAeB=eA+Be\frac{1}{2}[A,B] Homework Equations All are given above. The Attempt at a Solution I recently did a similar problem (show eABe-A = B + [A,B] + \frac{1}{2}[A,[A,b]]+...) by defining a function exABe-xA and...

So, am I doing this right? Starting with: Kx=λ'x where x=Lα Kx=KLα=LMLα ===> using K=LM =L(LM-1)α=LLMα-Lα ===>using [L,M]=1 =LKα-Lα Now going back to Kx=λ'x LKα-Lα=λ'Lα LKα=(λ'+1)Lα Finally, Kα=L-1(λ'+1)Lα since λ'+1 is a constant, Kα=(λ'+1)L-1Lα Kα=(λ'+1)α...

Homework Statement operators: K=LM and [L,M]=1 α is an eigenvector of K with eigenvalue λ. Show that x=Lα and y=Mα are also eigenvectors of K and also find their eigenvalues. Homework Equations K=LM [L,M]=1 Kα=λα The Attempt at a Solution I tried, but its not even worth...