Wavefunction hydrogen atom, table

The hierarchy of shells, subshells, and orbitals is summarized in Fig. 1.30 and Table 1.3. Each possible combination of the three quantum numbers specifies an individual orbital. For example, an electron in the ground state of a hydrogen atom has the specification n = 1, / = 0, nij = 0. Because 1=0, the ground-state wavefunction is an example of an s-orbital and is denoted Is. Each... 

All s-orbitals are independent of the angles 0 and c[>, so we say that they are spherically symmetrical (Fig. 1.31). The probability density of an electron at the point (r,0,ct>) when it is in a ls-orbital is found from the wavefunction for the ground state of the hydrogen atom. When we square the wavefunction (which was given earlier, but can also be constructed as RY from the entries for R and V in Tables 1.2a and 1.2b) we find that... 

Table 3.2 gathers some hydrogen atom wavefunctions. 

The mathematical forms of some of the wave functions for the H atom are listed in Table 1.2. Figure 1.5 shows plots of the radial parts of the wavefunction, R r), against distance, r, from the nucleus for the U and 2s atomic orbitals of the hydrogen atom, and Figure 1.6 shows plots of R r) against r for the 2p, 3p, 4p and 3d atomic orbitals the nucleus is at r = 0. 

Table 2. Gaussian expansion of the ground-state wavefunction for the D-dimensional hydrogen atom, a is the orbital exponent for M = 1. The remainder of the table defines the M — 9 expansion in the notation used in the text.

Generate the wavefunctions describing a hydrogen atom in the ground-state hyperfine sub-levels F=l,Mp> and F=0,Mp=0> using equation (3.55) and Table 3.3. Hence show that each of the matrix elements of the magnetic dipole moment operator between these sub-states has the value Ug. Evaluate equation (7.8) and calculate the radiative lifetime, in years, of the upper hyperfine level. 

Table 1.1 The wavefunctions obtained for a hydrogen-like atom, when n = 2. ...

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