Hydrogen-atom wave functions table

A list of the complete hydrogen atom wave functions is given in Table 22.2. 

TABLE 2.3 Hydrogen Atom Wave Functions Angular Functions... 

Table 1.1 Some wave functions for hydrogen and hydrogen-like atoms...

Table 6.2. Real wave functions for the hydrogen-like atom. The parameter a j,...

In a few cases, the wave-function F of a monatomic entity can be used for calculating a, e.g. 4.5 bohr3 for the hydrogen atom, or 0.205 A3 for the helium atom in agreement with the experimental value. Gaseous H does not have a Hartree-Fock function stable relative to spontaneous loss of an electron, and it is necessary to introduce correlation effects in order to calculate a which is said to be 31 A3. The value 1.8 A3 for H(-I) in Table 2 derives from NaCl-type LiH, NaH and KH. The anion B2Hg2 has a = 6.3 A3 to be compared with the isoelectronic C2H6 4.47 A3. Since CH4 has a =... 

Table 6.1. The first few m wave functions for the hydrogen atom...

Table 6.2. The first few radial wave functions R i(r) for the hydrogen atom (note that p = Zr/a0 where Ze is the nuclear charge)...

The modern view of the periodic table explains its structure in terms of an Aufbau procedure based on the wave-mechanical model of the hydrogen atom. Although seductive at first glance, the model is totally inadequate to account for details of the observed electronic configurations of atoms, and makes no distinction between isotopes of the same element. The attractive part of the wave-mechanical model is that it predicts a periodic sequence of electronic configurations readily specified as a function of atomic number. The periodicity follows from the progressive increase of four quantum numbers n, l, mi and s, such that... 

The solutions of the Schrodinger equation for the first three energy levels of the hydrogen atom are given in Table IV. The wave functions are expressed in terms of the spherical coordinates, r, the distance of the electron from the nucleus and the angles 6 and (f>. The relationship between spherical and Cartesian coordinates is seen in Figure 2. 

The sizes and shapes of the hydrogen atom orbitals are important in chemistry because they provide the foundations for the quantum description of chemical bonding and the molecular shapes to which it leads. Sizes and shapes of the orbitals are revealed by graphical analysis of the wave functions, of which the first few are given in Table 5.2. Note that the radial functions are written in terms of the dimensionless variable a, which is the ratio of Zr to ao- For Z = 1, a- = 1 at the radius of the first Bohr orbit of the hydrogen atom. 

Table 1 The energies of hydrogen atom confined to a box of radius R, obtained from numerical calculations, model wave functions, and the simple expression in Equation (3.39). For each state and R, the first row is from numerical calculation, the second row in brackets is from model wave function, and the third row in brackets is from the simple expression in Equation (3.39). The last column is the dipole polarizability for the ground state...

Table IV. Complete Wave Functions of the Hydrogen Atom...

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