Hydrogen atom energy states

Bohr Model of the Hydrogen Atom Energy States of the Hydrogen Atom Spectral Analysis... 

These ideas were so revolutionary that they would not have been accepted except for the fact that Bohr was able to propose a way to calculate exactly the energy levels for the hydrogen atom. Within ten years Bohr s calculational methods were completely replaced by better techniques, but his postulate that only certain atomic energy states are possible has been repeatedly shown to be correct. 

The H-73 basis set has been tested in the atomic calculation for hydrogen. The total energy of hydrogen atom in state was —0.4999951 a.u., which is superior... 

The conclusion of these comments is that the trial functions and the results reported in [3] do not provide a reliable description of the two-dimensional hydrogen atom ground-state energy for confinements by an angle and by a hyperbola. The solutions of the Schrodinger equation for the hydrogen atom confined by a hyperbola can also be constructed transparently and accurately using standard methods. 

Degeneracy. Are the hydrogen-atom energy levels degenerate For the bound states, the energy (6.94) depends only on n. However, the wave function (6.61) depends on all three quantum numbers n, I, and m, whose allowed values are [Eqs. (6.91), (6.92), (5.108), and (5.109)]... 

In 1971 a paper was published that applied the normalized variation function N exp(—brV o cr/ao) to the hydrogen atom and stated that minimization of the variational integral with respect to the parameters b and c yielded an energy 0.7% above the true ground-state energy for infinite nuclear mass. Without doing any calculations, state why this result must be in error. 

FIGURE 11.2 Atomic-orbital energies as a function of atomic number for neutral atoms, as calculated by Latter. [Figure redrawn by M. Kasha from R. Latter, Phys. Rev., 99,510 (1955). Used by permission.] Note the logarithmic scales. h is the ground-state hydrogen-atom energy, -13.6 eV. 

A FIGURE 6.12 Energy states in the hydrogen atom. Only states for / = 1 through / = 4 and n = oo are shown. Energy is released or absorbed when an electron moves from one energy state to another. 

---