On the second question, try to understand what eigenstates mean. The solution to the wave equation is very complex math, far above your level. But the idea is that these matter waves are mathematically only allowed for certain values of energy, and this model matches what is observed the the real atom's electrons.
I will be happy to critiue your thinking. Don't make matter waves over complicated to the point that you do not know what you are saying.
Describe the Bohr model of the atom. What is de Broglie's key idea (involving matter waves) that makes the Bohr atom have discrete energy levels?
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