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Complex conjugate energy

Note that here bracket does not mean just any round, square, or curly bracket but specifically the symbols and > known as the angle brackets or chevrons. Then ( /l is called a bra and Ivp) is a ket, which is much more than a word play because a bra wavefunction is the complex conjugate of the ket wavefunction (i.e., obtained from the ket by replacing all f s by -i s), and Equation 7.6 implies that in order to obtain the energies of a static molecule we must first let the Hamiltonian work to the right on its ket wavefunction and then take the result to compute the product with the bra wavefunction to the left. In the practice of molecular spectroscopy l /) is commonly a collection, or set, of subwavefunctions l /,) whose subscript index i runs through the number n that is equal to the number of allowed static states of the molecule under study. Equation 7.6 also implies the Dirac function equality... [Pg.114]

Star conjugation is essentially Hermitian conjugation followed by a complex conjugation of the complex energies (zi in the present case). [Pg.142]

Here r represents the coordinates for the system (x, y, z for each electron and each nucleus) and H is the Hamiltonian operator correspond ing to the total energy of the system. The integral is taken over the whole of configuration space for the system. if is the complex conjugate of if. [Pg.589]

Looking at the character tables for Gn, we see that the one-dimensional representations with complex characters are grouped in pairs, such that one set of characters is the complex conjugate of the other set, and each pair of one-dimensional representations is labeled E, indicating doubly degenerate energy levels. The reason for this practice is as follows. The... [Pg.213]

The terms with the eia> dependence merely lead to the complex conjugate of the above equation. Because the HF equation and energy are invariant to rotations among just occupied orbitals or among just virtual orbitals, we only need to consider the occupied-virtual block of d, i.e., d - and dj. Furthermore, if we assume the canonical HF wave function as an initial state, the zeroth-order quantities simplify to... [Pg.19]

Above, the equation for the total energy for a molecular system was expressed (these functions are real so the complex conjugate symbol may be dropped) ... [Pg.2731]

Note that the scalar product (10.5.13) does not involve complex conjugation and is therefore not positive definite. The final set of differential equations describing the motion of the helium resonances in the complex energy plane is identical with the set (4.1.57) with the only difference that the quantities appearing in (4.1.57) are now complex. [Pg.280]

V- Divergence operator V X Curl operator t Vector transposition t Complex conjugate The Variational Principle states that an approximate wave function has an energy which is above or equal to the exact energy. The equality holds only if the wave function is exact. The proof is as follows. Assume that we know the exact solutions to the Schrodinger equation. H. 1 = 0.1.2 oo CB.l)... [Pg.211]

The most stable MO real. In the order of increasing energy it is followed by complex conjugate pairs of MOs, i and < >, which are degenerate. If the number of atoms in the perimeter n is even, one has [Pg.77]


See other pages where Complex conjugate energy is mentioned: [Pg.19]    [Pg.197]    [Pg.19]    [Pg.197]    [Pg.175]    [Pg.184]    [Pg.117]    [Pg.138]    [Pg.203]    [Pg.8]    [Pg.135]    [Pg.131]    [Pg.213]    [Pg.368]    [Pg.463]    [Pg.252]    [Pg.255]    [Pg.105]    [Pg.418]    [Pg.38]    [Pg.185]    [Pg.45]    [Pg.291]    [Pg.340]    [Pg.99]    [Pg.469]    [Pg.472]    [Pg.232]    [Pg.344]    [Pg.270]    [Pg.39]    [Pg.93]    [Pg.248]    [Pg.532]    [Pg.575]    [Pg.333]    [Pg.157]    [Pg.162]    [Pg.78]    [Pg.12]   
See also in sourсe #XX -- [ Pg.197 ]




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