angular momentum operator

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1: 14.30 Spherical and Spheroidal Harmonics

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14.30.11 $$L^2{Y}_{l,m}={\mathrm{\hslash }}^{2}l(l+1)Y_{l,m},$$ $l=0,1,2,\mathrm{\dots }$,

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Symbols:

$Y_{l,m}(\theta ,\varphi )$: spherical harmonic, $m$: integer, $l$: nonnegative integer and $L$: angular momentum operator

Referenced by:

§18.39(ii)

Permalink:

http://dlmf.nist.gov/14.30.E11

Encodings:

pMML, png, TeX

See also:

Annotations for §14.30(iv), §14.30 and Ch.14

… ►Here, in spherical coordinates, $L^2$ is the squared angular momentum operator: ►

14.30.12 $$L^2=-{\mathrm{\hslash }}^2\left(\frac{1}{\sin \theta }\frac{\partial }{\partial \theta }\left(\sin \theta \frac{\partial }{\partial \theta }\right)+\frac{1}{{\sin }^2\theta }\frac{{\partial }^2}{{\partial \varphi }^2}\right),$$

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Defines:

$L$: angular momentum operator (locally)

Symbols:

$\frac{\partial f}{\partial x}$: partial derivative of $f$ with respect to $x$ , $\partial x$: partial differential of $x$ and $\sin z$: sine function

Referenced by:

§18.39(ii)

Permalink:

http://dlmf.nist.gov/14.30.E12

Encodings:

pMML, png, TeX

See also:

Annotations for §14.30(iv), §14.30 and Ch.14

►and ${\mathrm{L}}_z$ is the $z$ component of the angular momentum operator ►

14.30.13 $${\mathrm{L}}_z=-\mathrm{i}\mathrm{\hslash }\frac{\partial }{\partial \varphi };$$

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Defines:

${\mathrm{L}}_z$: $z$ component of the angular momentum operator (locally)

Symbols:

$\mathrm{i}$: imaginary unit, $\frac{\partial f}{\partial x}$: partial derivative of $f$ with respect to $x$ , $\partial x$: partial differential of $x$ and $z$: complex variable

Referenced by:

§14.30(iv), Erratum (V1.1.0) for Additions

Permalink:

http://dlmf.nist.gov/14.30.E13

Encodings:

pMML, png, TeX

Addition (effective with 1.1.0):

This equation was added.

See also:

Annotations for §14.30(iv), §14.30 and Ch.14

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2: 18.39 Applications in the Physical Sciences

… ►where ${\mathrm{L}}^2$ is the (squared) angular momentum operator (14.30.12). …

3: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►For fixed angular momentum $\mathrm{\ell }$ the appropriate self-adjoint extension of the above operator may have both a discrete spectrum of negative eigenvalues ${\lambda }_n,n=0,1,\mathrm{\dots },N-1$, with corresponding $L^2([0,\mathrm{\infty }),r^{2}dr)$ eigenfunctions ${\varphi }_n(r)$, and also a continuous spectrum $\lambda \in [0,\mathrm{\infty })$, with Dirac-delta normalized eigenfunctions ${\varphi }_{\lambda }(r)$, also with measure $r^{2}dr$. …

4: Brian R. Judd

… ►Judd’s books include Operator Techniques in Atomic Spectroscopy, published by McGraw-Hill in 1963 and reprinted by Princeton University Press in 1998, Second Quantization and Atomic Spectroscopy, published by Johns Hopkins in 1967, Topics in Atomic and Nuclear Theory (with J. … Elliott), published by Caxton Press in 1971, and Angular Momentum Theory for Diatomic Molecules, published by Academic Press in 1975. …

5: Bibliography J

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Derivation of Green-type, transitional and uniform asymptotic expansions from differential equations. V. Angular oblate spheroidal wavefunctions ${\overline{ps}}_n^r(\eta ,h)$ and ${\overline{qs}}_n^r(\eta ,h)$ for large $h$ . Proc. Roy. Soc. London Ser. A 321, pp. 545–555.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§30.9(ii).

Encodings:

BibTeX

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Angular Momentum Theory for Diatomic Molecules. Academic Press, New York.

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External Links:

ISBN 0-12-391950-9

Referenced by:

§30.12, §34.12, Profile Brian R. Judd.

Encodings:

BibTeX

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Operator Techniques in Atomic Spectroscopy. Princeton University Press, Princeton, NJ.

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External Links:

ISBN 0-691-05901-2

Referenced by:

§34.12, Profile Brian R. Judd.

Encodings:

BibTeX

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6: Bibliography B

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Some Geometric Aspects of Wave Motion: Wavefront Dislocations, Diffraction Catastrophes, Diffractals. In Geometry of the Laplace Operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979), Vol. 36, pp. 13–28.

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External Links:

MathReview (I. Stewart), ZentralBlatt

Referenced by:

§36.14(i).

Encodings:

BibTeX

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Prolate angular spheroidal wave functions. Comput. Phys. Comm. 30 (2), pp. 187–192.

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External Links:

Document, Code

Referenced by:

1st item.

Encodings:

BibTeX

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Angular Momentum in Quantum Physics: Theory and Application. Encyclopedia of Mathematics and its Applications, Vol. 8, Addison-Wesley Publishing Co., Reading, M.A..

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External Links:

ISBN 0-201-13507-8, MathReview (Kurt Bernardo Wolf), ZentralBlatt

Referenced by:

§34.14.

Encodings:

BibTeX

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Quantum Theory of Angular Momentum. A Collection of Reprints and Original Papers. Academic Press, New York.

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External Links:

ISBN 0-12-096056-7, MathReview (R. Mirman)

Referenced by:

§34.12, §34.3(v), §34.5(v), §34.7(v).

Encodings:

BibTeX

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Angular Momentum. 3rd edition, Oxford University Press, Oxford.

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External Links:

ISBN 0-19-851759-9

Referenced by:

§34.9.

Encodings:

BibTeX

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