Does energy conservation hold if eigen-energies are multiplied by probabilities?

[Opi_Phys]

Hello,

let us suppose that we have a quantum harmonic oscillator being in the first exciting state. It means that system has some definite energy E_1. Than we change force constant of of the oscillator. As a consequence eigen states and there energy are changed. I think that after this change system cannot be in some new eigen state. Because in this case the system would have some new definite value of energy and we would have contradiction with conservation low. So I conclude that after force constant is changed system will be in some superposition of new eigen states. It means that making measurement we can with some probability find the system in some state having some energy. I have two question. Does the energy conservation low implies that sum of eigen-energies multiplied on the probability to find system in the corresponding state should be equal to the initial energy of the system (e_1*v_1 + e_2*v_2 + ... e_n*v_n = E_1)? Let us suppose that we made measurement and the find system in some new eigen-state with energy e_k. How to be with the conservation low? I mean e_k is not equal to E_1 and it should be a problem?

Opi.

 

[Opi_Phys]

I think my questions can be formulated in shorter way:

1. If state of a system is a superposition of the eigen state, how is defined total energy of the system?

2. Should energy conservation low work for this quantum mechanical energy?

3. If energy conservation low is satisfied, is it satisfied statistically (by averaging over many measurements)?

 

[Opi_Phys]

Here is the same question asked in the google-group. In one day after question was asked there were written more useful information.

http://groups-beta.google.com/group...c351f/a206fcbc09b95c16?hl=en#a206fcbc09b95c16