Superposition of quantum states There has been many questions asked about superposition on this forum, but none of them provided me with a satisfactory answer for my following question.
I understand, quite well, the principle of superposition as a mathematical concept. I also understand quite well the superposition of wave functions of probability amplitudes. 
However, there is a specific example where I have trouble figuring it out.

Dirac wrote: "A measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured, the eigenvalue this eigenstate belongs to being equal to the result of the measurement."

In the case of a spin-half particle in a magnetic field, the eigenstate of the Hamiltonian matrix for the z-spin corresponds to a given discrete spin value, so I have no problem imagining an electron in a state $|ψ>$ jumping to a state $|+>$.
Now, in the case of the simplified model of the 2 states of an ammonia molecule(nitrogen above or below the hydrogens), as presented by Feynman in chapters 8 and 9 of his lectures, the eigenstate correspond to a superposition of the up and down states (and if it starts in state $|1>$, its probability amplitude will oscillate in between 0 and 1 until it emits enough energy to settle in the lower energy state,$E_{0}-A$.
So my question is: How can the system jump (upon measurement) to an eigenstate which is a superposition of the up and down geometrical states, when in fact, it is possible to measure the angles of its tetrahedral conformation in experiments: geometrically, the nitrogen has to be above or below, it can't be in a flat plane,can it? Does it have anything to do with Heisenberg's uncertainty principle,especially the uncertainty associated to its position?
As per comments below, I'll provide more details on my question:
Feynman shows the 2 geometrical states as |1> and |2>, and the 2 energy eigenstates as |I> and |II>. Each eigenstate's probability amplitude is a superposition of the 2 geometrical states' probability amplitudes, and conversely, each geometrical state is in a superposition of the energy eigenstates. The upper eigenstate has energy E+A, and the lower one E-A. If the molecule "starts" in the state |1>, then it is in a superposition of the 2 eigenstates, which have different frequencies ((E+A)/h and (E-A)/h respectively), so the molecule will switch between |1> and |2> at the frequency A/h. Since its eigenstate is not a geometrical state, I'm wondering where we would actually find it if we could observe it? From the answer below, I guess we can't differentiate between the 2 geometrical states because of Heisenberg's uncertainty principle?
Also, since we're on the subject: are the superposition of probability amplitudes and the superposition of quantum states 2 different concepts, or are they 2 ways to see the exact same thing?
 A: It is, indeed, possible that when the ammonia molecule is in an energy eigenstate, it is in a superposition of the "geometrical" nitrogen (N) up or down state. As you suspect correctly, this is a case of Heisenberg's uncertainty principle for the observables N position and energy. Energy and N position are observables that cannot be both accurately measured. If the molecule is in an energy eigenstate E1, its N up or down state is undetermined (probability 50% up and 50% down). Conversely, if the molecule is in an N up eigenstate, its energy is undetermined (50% probability E1 and 50% E2). 
There are other simple quantum systems with similar behavior. For example the linear photon polarizations vertical and horizontal and the circular polarizations right circular and left circular. When a photon has e.g. vertical polarization, it is in a superposition of 50% probability right and 50% left circular polarization. Conversely, when it has a right circular polarization, it is in a superposition of 50% probability vertical and 50% horizontal polarizations.This is due to the fact that the observables linear and circular polarizations cannot be simultaneously measured accurately. This is also due to Heisenberg's uncertainty principle.  
A: The ammonia molecule’s inversion can be modelled, based on the energy change during its "umbrella" inversion. This involves a double potential well with a central barrier that corresponds to the energy required to get to the intermediate flat configuration. 
This results in adjacent symmetric (+) and anti-symmetric (-) harmonic oscillator states with a very small energy difference, resulting in the two states being about equally populated at room temperature and accessible to each other by quantum mechanical tunnelling. 
ADDITIONALLY (re your “wondering where we would actually find it if we could observe it”): From the  csbsju.edu  link below: 
"If |NH3> represents the left-hand well and |H3N> the right-hand well, we can write the wave functions for these states symbolically as shown below.
|Psi>0 = 2^(-1/2) [|NH3> + |H3N>]     and      |Psi>1 = 2^(-1/2) [|NH3> - |H3N>]
[snip] However, |Psi>1 can be separated from |Psi>0 by electrostatic means and directed to a resonant cavity." 
According to http://www.users.csbsju.edu/~frioux/super/MM-super.htm the states constitute "one-particle" superpositions in which a single particle or system is assumed to occupy a linear superposition of two states.[As Freecharly pointed out, it's not the whole molecule in a superposition.]  
The bond angles are the same in both observable states (I think one can say that they won't be observed in the intermediate/transitional - flat configuration - that you're concerned about). See How are bond angles determined?
Two factors contribute to the rapidity of the inversion: a low energy barrier and a narrow width of the barrier itself. 
Ammonia therefore exhibits a quantum tunnelling due to a narrow tunnelling barrier (rather than being the result of thermal excitation). As you seem to have realised, this is related to Heisenberg's Uncertainy Principle.
Superposition of the two states leads to energy level splitting, which is used in ammonia masers.
Hoping this helps.
