DLMF:14.30.E11 (Q4973)

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DLMF:14.30.E11
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    Statements

    Defining formula
    L 2 ⁢ Y l , m = ℏ 2 ⁢ l ⁢ ( l + 1 ) ⁢ Y l , m , superscript L 2 spherical-harmonic-Y 𝑙 𝑚 superscript Planck-constant-over-2-pi 2 𝑙 𝑙 1 spherical-harmonic-Y 𝑙 𝑚 {\displaystyle{\displaystyle\mathrm{L}^{2}Y_{{l},{m}}=\hbar^{2}l(l+1)Y_{{l},{m% }},}}
    0 references
    DLMF id
    DLMF:14.30.E11
    0 references
    Symbols used
    spherical harmonic
    Defining formula
    Y l , m ⁡ ( θ , ϕ ) spherical-harmonic-Y 𝑙 𝑚 𝜃 italic-ϕ {\displaystyle{\displaystyle Y_{{\NVar{l}},{\NVar{m}}}\left(\NVar{\theta},% \NVar{\phi}\right)}}
    xml-id
    C14.S30.E1.m2ahdec
    0 references
    Q11641
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S30.XMD1.m1idec
    0 references
    Q11642
    Defining formula
    l 𝑙 {\displaystyle{\displaystyle l}}
    xml-id
    C14.S30.XMD2.m1idec
    0 references
    angular momentum operator (locally)
    Defining formula
    L L {\displaystyle{\displaystyle\mathrm{L}}}
    xml-id
    C14.S30.XMD4.m1dec
    0 references
     
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