- #1

koroljov

- 26

- 0

Imagine a hydrogen atom.

An electron is sitting nicely in its orbital. I measure its quantum numbers to know in which orbital it is. It will remain there for now, since the orbitals are eigenfunctions of the hamiltonian.

Now I decide to measure the position of the electron. So, I use the position operator (x,y,z). The eigenfunctions of this operator are Dirac functions (they are, aren't they?). So, the wavefunction now "collapses" into a dirac function. This dirac function can be expanded as a linear combination of the orbital functions (since these are orthonormal and complete).

So, when I measure the quantum numbers of the electron once again, I will have a nonzero chance of finding the electron in any of the orbitals which made a nonzero contribution to the expansion of the dirac function. Therefore, I might find the electron in an orbital with more or less energy than the one in which it was originally.

Where did that energy come from? Or, alternatively, where did it go to? Did I add or remove energy to/from the electron by trying to measure its position? Or is there some foolish error in the above reasoning?