Hydrogen atom wavefunctions

Table 3.2 gathers some hydrogen atom wavefunctions. 

There are a number of different ways of representing hydrogen-atom wavefunctions graphically. We will illustrate some of these with the I5 ground state. In atomie units,... 

P8.5 The hydrogen atom wavefunctions are obtained from the solution of the Schr6dinger equation in Chapter 10. Here we need only the wavefiinction that is provided. It is the square of the wavefimction that is related to the probability (Section 8.4). 

In the continuum limit a K) —> 0) eqn (E.3) is identical to the effective one-dimensional equation for the radial part of the three-dimensional hydrogen atom wavefunction, u r) = r (r), for the case of zero angular momentum, where 4> r) is the radial wavefunction (see Cohen-Tannoudji et al. (1977, p. 792)). This equation was studied in detail by Loudon (1959). It is useful to treat the even and odd parity solutions separately. 

Consider the following expressions, where t/f is a hydrogen-atom wavefunction. 

Plots of 4Trr Rf versus distance for other hydrogen atom wavefunctions, as labeled. There is a simple relationship between the quantum numbers and the number of radial nodes. 

The complete designation for a hydrogen atom wavefunction will include the intrinsic spin eigenstate M/n,i.m.o or... 

One possibility as a basis set of functions to be used for/is the hydrogen-atom functions. As seen in the case of a helium atom, this is not a particularly good start. The hydrogen-atom wavefunctions do not account for shielding and other affects of the inter-electronic repulsion. A basis set of functions that take this into account is a much better starting point for the calculation. J. C. Slater created such a basis set of functions known as the Slater-type orbitals (STO). The functions have the following general form. 

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