For a one-electron atom in free space what would be the, Physics

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For a one-electron atom in free space what would be the

1. What is the fundamental reason why the size of the hydrogen atom in its ground state has the value it does?

2. For a one-electron atom in free space, what would be the mathematical consequences of changing the choice of direction of the z axis? The physical consequences? What if the atom is in an external electric or magnetic field?

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