Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Algebraic solutions for all dihedral groups (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 8196-8222 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The significant problem with using point groups is the dependence upon extensively tabulated results. We present simple algebraic expressions for the primitive characters, matrix irreps, symmetry adapted functions (SAFs), and Clebsch–Gordan coefficients for all dihedral groups, Dn, Cnv, Dnd, and Dnh. Those results, for arbitrary n and for single- and double-valued representations, have been derived in a simple manner without using group tables. Previously incomplete tabulated results are now redundant. In particular the parity dependence of the SAFs of the improper dihedral groups is shown analytically. Simple relations are derived between the SAFs of the proper and improper dihedral groups, so that the SAFs of the latter can be easily obtained from the SAFs of Dn. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1286513
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Algebraic solutions for point groups: The tetrahedral group for the group chain T⊃C3 (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 467-488 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new technique, the double-induced technique, is introduced for constructing irreducible symmetry operators (ISO's) adapted to the group chain G⊃G(s). Simple algebraic expressions of irreducible matrices, the ISO's and symmetry adapted functions (SAF's) are derived for the group chain T⊃C3 for both single-valued and double-valued representations in a unified way. The simplicity of the results lies in the fact that the ISO's and SAF's are functions of only the quatum numbers of the group chain [the analogy of (j,m) for the group chain SO3⊃SO2], without involving any irreducible matrix elements. The symmetries of the SAF's are disclosed for the first time. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532320
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Algebraic expressions for irreducible bases of icosahedral group (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 387-410 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The recently discovered point-group symmetrized boson representation (SBR) is constructed for the icosahedral group Ih. With the aid of the SBR, succinct algebraic expressions for the irreducible bases and irreducible matrices have been found. Irreducible bases for non-regular representations can be found easily from those of the regular representation without projections. Explicit expressions of the irreducible bases are given for the molecule B12H12 for several important cases. It is shown that, far from being "chaotic" in structure, the 120 irreducible matrices of Ih have a high degree of symmetry in that the 14 400 entries can be reproduced from a few dozen entries according to three rules. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531855
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    The induction coefficients of the Hecke algebra and the Clebsch–Gordan coefficients of the quantum group SUq(N). II. General Gel'fand basis (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4316-4329 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Clebsch–Gordan coefficients for the general Gel'fand basis of the quantum group SUq(N) are calculated from the induction coefficients of the Hecke algebra Hf(q) by the linear equation method. The advantage of this method is that the calculation of the SUq(N) Clebsch–Gordan coefficients is rank independent. The SUq(N) Clebsch–Gordan coefficients for the resulting irreps [f1,f2,f3] with f1+f2+f3≤4 are tabulated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530002
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    The induction coefficients of the Hecke algebra and the Clebsch–Gordan coefficients of the quantum group SUq(N). I. Special Gel'fand basis (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4305-4315 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general procedure for evaluating the induction coefficients (IDCs) or the outer-product reduction coefficients of the Hecke algebra Hf(q) of the Af−1 type is formulated based on the linear equation method. Analytical expressions for the IDC's of Hf(q) are tabulated for f≤4. It is also proved that these IDCs are the Clebsch–Gordan coefficients for the special Gel'fand basis of the quantum group SUq(N).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530001
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Algebraic solutions for point groups: The tetrahedral group for the group chain T⊃D2⊃C2 (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5502-5518 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A factorization lemma is discovered for the irreducible symmetry operators (ISO's) of a semidirect product group of two abelian groups. By means of it, simple algebraic expressions of the T⊃D2 single-valued irreducible matrices, ISO's and symmetry adapted functions are derived. Using the double-induced technique, the algebraic solutions for the double-valued representations of group T in the group chain T⊃C2 are also obtained. The simplicity and elegance of the algebraic solution of the point group can be compared with that of the analytic solution of the rotation group. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532547
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Application of the eigenfunction method to the icosahedral group (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1065-1075 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The group table for the icosahedral group I is constructed by using the isomorphism between the group I and a subgroup of the permutation group S12. The single-valued irreducible representations and Clebsch–Gordan (CG) coefficients of I are calculated by a computer code based on the eigenfunction method. The irreducible matrix elements for all the 60 group elements are given explicitly in the form of (m/n)1/2[exp(iφ)]p [2 cos φ]q [2 cos 2φ]r, where m, n, p, q, and r are integers and φ=2π/5. The Clebsch–Gordan coefficients of I are all real under a new phase convention for time reverse states and tabulated in the form of (m/n)1/2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528784
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    The method of symmetrized bosons with applications to vibrations of octahedral molecules (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 815-825 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new technique for constructing representations of point groups, called symmetrized boson representation is introduced. This method is particularly useful when describing vibrations of large molecules and for high overtones. The method is illustrated by applying it to stretching overtones of octahedral molecules, SF6, WF6, and UF6 with group Oh. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.470807
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    Algebraic expressions of the Clebsch-Gordon coefficients of the point group T† (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5519-5535 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A method for finding algebraic expressions of the Clebsch-Gordan (CG) coefficients of point groups is proposed and applied to the tetrahedral group. It is shown that in constructing the CG coefficients the irreducible symmetry operator (ISO) of a double group G† can be replaced by an effective ISO which is much simpler than the usual ISO. The effective ISO for the group chain T†⊃C3† is Pμ,μ¯(λ)=δμμ¯+3dμμ¯(λ)(C2z)*C2z, where d(λ)(C2z) is the matrix of C2z in the irrep λ of T†. With this effective ISO and the algebraic expression of d(λ)(C2z), the algebraic expressions are derived for the real CG coefficients of T† in the group chain T†⊃C3†. The algebraic expressions for the complex (real) CG coefficients of the group chain T†⊃D2†⊃C2† (T†⊃C2†) have also been obtained. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532548
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Point-group symmetrized boson representation. Algebraic solution for symmetry-adapted bases of Oh (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 2400-2425 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A point group symmetrized boson representation (SBR) is introduced that is particularly convenient for describing molecular vibrations. In this paper the SBR is elucidated using the example of the molecule SF6 with Oh symmetry. The advantages of the SBR are that its basis vectors have a clear physical picture, their number is very small (equal to one-eighth of the dimension of the reducible representation for Oh), and the irreducible bases for any concrete cases can be obtained trivially from those for the general case without any projection. All the irreducible bases for the group chains Oh&supuline;D4&supuline;C4 or Oh&supuline;D4&supuline;D2 are tabulated once and for all. As an application, the Hamiltonian in the algebraic model of Iachello and Oss for stretching vibrations of the molecule SF6 is diagonalized in the symmetry adapted bases. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531518
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...