Abstract
In the last section, we calculated the matrix elements of the operators, L x , L y , L z . These operators are functions only of θ, φ, and ∂/∂θ, ∂/∂φ.It will also be extremely useful to have the matrix elements of the angular parts of the position vector of the particle, viz. x/r = sin θ cos φ, y/r = sinθ sin φ, and z/r = cos θ. To get these, it would be useful to interchange the role of the quantum numbers l, and m, in the factorization method and derive expressions for ladder operators changing l to l ± 1, keeping m fixed.
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© 2000 Springer Science+Business Media New York
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Hecht, K.T. (2000). ℓ-Step operators for the θ Equation. In: Quantum Mechanics. Graduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1272-0_9
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DOI: https://doi.org/10.1007/978-1-4612-1272-0_9
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