Orbital angular momentum ladder operators

In Chapters 4, 5, and 6 the Schrodinger equation is applied to three systems the harmonie oseillator, the orbital angular momentum, and the hydrogen atom, respectively. The ladder operator technique is used in each case to solve the resulting differential equation. We present here the solutions of these differential equations using the Frobenius method. 

The orbital angular momentum quantum number 1 can take the values 0,1,2,3,... (also know as azimuthal quantum number) and the magnetic quantum number m must be in —/, — / + 1,..., / (also known as orientational quantum number). The eigenfunctions can be efficiently constructed through the definition of ladder operators, which is standard in nonrelativistic quantum mechanics and therefore omitted here. The general expression for the spherical harmonics reads [70]... 

PROBLEM 3.5.6. One can define linear ladder operators for angular momentum (orbital or spin) the raising operator + = Lx + iLy and the lowering operator =LX — iLy. (a) Verify that brute-force expansion yields + =... 

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