When you measure position of an electron in a energy pure state, what happens to the energy? When you measure the position of an electron that is in a pure energy state, what happens the energy becomes non-deterministic. That is future measurements of energy can only be predicted with respect to a probability distribution. 
This seemingly violates the conservation of energy since future measurements of energy may give different results. 
I assume here that the measurement process somehow adds some non-determinism or transfers energy to the measuring apparatus. But this is just a vague idea. How do you clearly explain this?
 A: 
When you measure the position of an electron that is in a pure energy state, what happens the energy becomes non-deterministic.

An electron in a pure energy state is in a bound state. To "measure it" you have to excite it or , if it is in an already excited state measure the photon of its deexcitation. 
You cannot measure its position, while bound, to an accuracy greater than the location of the atom in the crystal whence it came , in any case the Heisenberg uncertainty principle  (HUP)holds for all these measurements. 
In this bubble chamber photo

the detached spiral on the left is an electron kicked off form a hydrogen atom of the liquid hydrogen bubble chamber. You could measure its starting point but with accuracies of micron and energies of kev the Heisenberg uncertainty principle will be fully satisfied.

That is future measurements of energy can only be predicted with respect to a probability distribution.

This probability distribution in our instruments and sizes of working is definitive enough. These matters become important for nano technology issues when the sizes are comsensurate with the orders of magnitude of the uncertainty principle.

This seemingly violates the conservation of energy since future measurements of energy may give different results. 

I do not see any violation of energy conservation in atom photon interactions, except within the bounds of the HUP. Conservation of energy is bounded by the HUP, which is the gross envelope of what probability distributions for quantum mechanical entities/particles in interaction  mean. 
A: If you're looking for a general solution to the schrodinger equation then yes, it is possible for the atom to be in a superposition of energy states. This does not violate conservation of energy. Can you see why? It is a subtle point.
To start you off -- how do you measure the position of the electron in the first place? You must hit it with something. This "something" is also quantum mechanical, and hence can exist in a superposition of energy states...
A: If your electron is in a pure state then it's an eigenfunction, $\psi_e$, of the Hamiltonian describing it, $H_e$. The measuring system will also, in principle at least, be described by some wavefunction, $\psi_m$. If the two don't interact then the total wavefunction will just be a product:
$$ \Psi = \psi_e\psi_m $$
and the system won't change with time. But if the electron and measuring system don't interact there's no way you can measure the electron energy. For a measurement to be possible there must be some interaction, and that means the Hamiltonian describing the electron changes. because the Hamiltonian is no longer $H_e$ the wavefunction $\psi_e$ is no longer an eigenfunction. Likewise $\psi_m$ is no longer an eigenfunction of the measurement system and the total wavefunction will no longer be separable:
$$ \Psi \ne \psi_e\psi_m $$
The electron no longer has a well defined energy because we can only talk about the energy of the whole system $\Psi$.
In principle the electron and measuring system will become entangled and exist in a superposition of states. However in the real world the entangled system will rapidly decohere and we'll end up with a system that is once again separable:
$$ \Psi = \psi'_e\psi'_m $$
But generally $\psi_e \ne \psi'_e$ and $\psi_m \ne \psi'_m$. Both the electron and the wavefunction will have been changed by the measurement process so we would expect that their energies have changed. Eneergy has been transferred from the measuring system to the electron or vice versa. So the electron energy is not conserved. However the total energy is still conserved.
