Part 2 and Part 1 of this essay can be found by following the former links.
Conclusions:
1. Like its real counterpart hydrogen the gedanken experiment of one dimensional hydrogen atom (1D H) shows bound states. A scattered electron state only occurs for zero energy, at infinite distance from the proton.
2. the 1D H atom has non-zero ground state energy.
3. The wavefunctions of the 1D H atom are governed by a single quantum number (n)
4. The wave functions of quantum number n show n+1 nodes (zero points).
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