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Non-degenerate

Jahn-TeHer effect The Jahn-Teller theorem states that, when any degenerate electronic slate contains a number of electrons such that the degenerate orbitals are not completely filled, the geometry of the species will change so as to produce non-degenerate orbitals. Particularly applied to transition metal compounds where the state is Cu(II)... [Pg.229]

In any experiment, tlie probability of observing a particular non-degenerate value for the system property A can be detemiined by the following procedure. First, expand the wavefiinction in temis of the complete set of nomialized eigenfimctions of the qiiantmn-niechanical operator,... [Pg.9]

The one-dimensional cases discussed above illustrate many of die qualitative features of quantum mechanics, and their relative simplicity makes them quite easy to study. Motion in more than one dimension and (especially) that of more than one particle is considerably more complicated, but many of the general features of these systems can be understood from simple considerations. Wliile one relatively connnon feature of multidimensional problems in quantum mechanics is degeneracy, it turns out that the ground state must be non-degenerate. To prove this, simply assume the opposite to be true, i.e. [Pg.20]

The principle of tire unattainability of absolute zero in no way limits one s ingenuity in trying to obtain lower and lower thennodynamic temperatures. The third law, in its statistical interpretation, essentially asserts that the ground quantum level of a system is ultimately non-degenerate, that some energy difference As must exist between states, so that at equilibrium at 0 K the system is certainly in that non-degenerate ground state with zero entropy. However, the As may be very small and temperatures of the order of As/Zr (where k is the Boltzmaim constant, the gas constant per molecule) may be obtainable. [Pg.373]

If //is 00 (very large) or T is zero, tire system is in the lowest possible and a non-degenerate energy state and U = -N xH. If eitiier // or (3 is zero, then U= 0, corresponding to an equal number of spins up and down. There is a synnnetry between the positive and negative values of Pp//, but negative p values do not correspond to thennodynamic equilibrium states. The heat capacity is... [Pg.403]

The constant of integration is zero at zero temperature all the modes go to the unique non-degenerate ground state corresponding to the zero point energy. For this state S log(g) = log(l) = 0, a confmnation of the Third Law of Thennodynamics for the photon gas. [Pg.411]

Whenever a fiinction can be written as a product of two or more fiinctions, each of which belongs to one of the synnnetry classes, the symmetry of the product fiinction is the direct product of the syimnetries of its constituents. This direct product is obtained in non-degenerate cases by taking the product of the characters for each symmetry operation. For example, the fiinction xy will have a symmetry given by the direct product of the syimnetries of v and ofy this direct product is obtained by taking the product of the characters for each synnnetry operation. In this example it may be seen that, for each operation, the product of the characters for Bj and B2 irreducible representations gives the character of the representation, so xy transfonns as A2. [Pg.1136]

Each such nonual mode can be assigned a synuuetry in the point group of the molecule. The wavefrmctions for non-degenerate modes have the following simple synuuetry properties the wavefrmctions with an odd vibrational quantum number v. have the same synuuetry as their nonual mode 2the ones with an even v. are totally symmetric. The synuuetry of the total vibrational wavefrmction (Q) is tlien the direct product of the synuuetries of its constituent nonual coordinate frmctions (p, (2,). In particular, the lowest vibrational state. [Pg.1137]

A. Term Symbols for Non-Degenerate Point Group Symmetries... [Pg.265]

Notiee that the eigenvalue )ik = 3 appears twiee we say that the eigenvalue )ik = 3 is doubly degenerate. )ik = 2 is a non-degenerate eigenvalue. [Pg.529]

Henee, for this non-degenerate root, one is able to solve for all of the vj elements in terms of one element that is yet undetermined. [Pg.529]

Asimple example is the formation of the hydrogen molecule from two hydrogen atoms. Here the original atomic energy levels are degenerate (they have equal energy), but as the two atoms approach each other, they interact to form two non degenerate molecular orbitals, the lowest of which is doubly occupied. [Pg.49]

The character tables for all important point groups, degenerate and non-degenerate, are given in Appendix A. [Pg.92]

Inspection of this character table, given in Table A. 12 in Appendix A, shows two obvious differences from a character table for any non-degenerate point group. The first is the grouping together of all elements of the same class, namely C3 and C as 2C3, and (t , and 0-" as 3o- . [Pg.92]

The + 1 and —1 characters of the and A2 species have the same significance as in a non-degenerate point group. The characters of the E species may be understood by using the... [Pg.92]

Except for the multiplication of by we follow the rules for forming direct products used in non-degenerate point groups the characters under the various symmetry operations are obtained by multiplying the characters of the species being multiplied, giving... [Pg.95]

In Table B. 1 in Appendix B are given formulae, analogous to those derived for the C2 point group, for determining the number of normal vibrations belonging to the various symmetry species in all non-degenerate point groups. [Pg.165]

In a molecule belonging to a degenerate point group, for example C, , the non-degenerate vibrations of the various sets of equivalent nuclei can be treated as in Section 6.2.2.1. [Pg.165]

There are simple symmetry requirements for the integral of Equation (6.44) to be non-zero and therefore for the transition to be allowed. If both vibrational states are non-degenerate, the requirement is that the symmetry species of the quantity to be integrated is totally symmetric this can be written as... [Pg.168]


See other pages where Non-degenerate is mentioned: [Pg.20]    [Pg.186]    [Pg.223]    [Pg.381]    [Pg.402]    [Pg.406]    [Pg.1134]    [Pg.1142]    [Pg.165]    [Pg.165]    [Pg.184]    [Pg.265]    [Pg.266]    [Pg.318]    [Pg.319]    [Pg.529]    [Pg.570]    [Pg.570]    [Pg.571]    [Pg.578]    [Pg.87]    [Pg.87]    [Pg.87]    [Pg.91]    [Pg.92]    [Pg.163]    [Pg.163]    [Pg.168]    [Pg.172]    [Pg.173]    [Pg.276]    [Pg.277]   
See also in sourсe #XX -- [ Pg.65 ]




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