- #1

fog37

- 1,568

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Could anyone offer some insight on this topic?

In the case of a physical system composed of multiple particles, there is only one single wavefunction that depends on the three position variables of each particle and the parameter time t. For example, in the case of 2 particles, we have

$$\Psi(r_1, r_2, t)$$

where ##r_1=(x_1,y_1,z_1)## and ##r_2=(x_2,y_2,z_2)##.

- For the hydrogen atom, there is only electron which can be in one particular state (among the many) or in a superposition of multiple states. A state that hosts a single electron is called
**orbital**, correct?

- For a system with
**two**electrons, if we apply the approximation that the electrons are not interacting, we can express the two-particle wavefunction as a product of single electron wavefunctions, i.e. orbitals. These orbitals can be eigenstates of a certain observable. The non-interaction seems to be a strong approximation. Because of indistinguishability, we don't know which particle is in which mono-electronic (orbital) state.

- In the case of
**entanglement**between two particles, we say that total state describing the two particle can actually not be expressed as a product of orbital states, i.e. the wavefunction cannot be factorized, correct? In general, even without entanglement, we cannot tell in which state each particle may be (that is due to the fact that the particles are identical and indistinguishable).

- Entanglement is about the existence of a
*correlation*between the observables associated to each one of the two particles. Correlation means that if we know the value of the observable for one particle we automatically know the value of the observable for the other particle. For instance, if particle 1 is in state ##|+>##, particle 2 will be for sure in state ##|->##. If particle 1 is in state##|->## , particle 2 will be in state ##|+>##. What if the entangled observables have more than two possible values?

- For two possible values of the observables, the two particle can be either in the state ##|+ - >## or ##|- - > ## or even a superposition state |Phi>= c_1* ##|+ -> + c_2*|- +>##. When the two particle are in the superposition state c_1* ##|+ -> + c_2*|- +>##, we say they are entangled because the physical state of one of the particles on its own does not exist. Only the ‘pair state’ exists. But isn't that the case also for a multiple particles system having just a single total wavefunction (if we don't apply the non-interaction approximation) even without entanglement? Entangled particles and interacting particles are not the same thing but their total wavefunctions seem to not be deconstructed in a product of single particle wavefunctions...

Thanks,

Fog37