Image »Lz of the Quantum Mechanical Angular Momentum Precisely Determined But Lx and Ly Not« download
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The \( L_{\text z} \) component of the total orbital angular momentum \( \class{green}{\boldsymbol{L}} \) of a quantum mechanical system is precisely determined and has the value: \( L_{\text z} = \class{violet}{m} \, \hbar \).
The \(L_{\text y}\) and \(L_{\text x}\) components of the total angular momentum \( \class{green}{\boldsymbol{L}} \) are indeterminate due to Heisenberg's uncertainty principle. The exemplarily drawn angular momentum \( \class{green}{\boldsymbol{L}} \) could lie somewhere rotationally symmetric around the \(L_{\text z}\) axis on the cone and have the same \(L_{\text z}\) component.
