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Edge5
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Edge5 said:Hello, I don't understand how can electrons in triplet state can have the same value of spin? Shouldn't the spins be different because two fermions can't have the same state?
The following picture explain my question in more detail.
View attachment 234567
Thank you for clarifiying this issue :)ShayanJ said:That's because the spin state is not the only part of the state. Any degree of freedom in a quantum system will have a vector from an appropriate Hilbert state associated to it which describes the state of that degree of freedom. The full state is a tensor product of all the states of all degrees of freedom. For example if we consider that in this case, there are only spin and spatial degrees of freedom, then the full state of two fermions would be ##|\Psi(1,2)\rangle=|\Delta(1,2)\rangle_{spin} \otimes |\Phi(1,2)\rangle_{spatial} ##. it is the overall state that has to be completely antisymmetric for any finite number of fermions, but each part can be symmetric which means the other part has to be antisymmetric.
Edge5 said:Can you also explain why we don't have a singlet state as I wrote in the question?
Edge5 said:Can you also explain why we don't have a singlet state as I wrote in the question?
In quantum mechanics, electrons have a property called spin, which is a fundamental characteristic that determines their behavior. In a triplet state, two electrons occupy the same energy level and have the same spin, meaning they have the same intrinsic angular momentum. This is possible because of the Pauli exclusion principle, which states that no two electrons can have the same set of quantum numbers, including spin, in the same energy state.
The fact that electrons can have the same spin in triplet state is significant because it allows for certain chemical reactions to occur. For example, in photosynthesis, the simultaneous absorption of two photons by two electrons in a triplet state is necessary for energy transfer to occur.
The spin of electrons in a triplet state is determined by the orientation of their magnetic moments. This can be measured using various techniques, such as electron spin resonance or nuclear magnetic resonance.
No, in a triplet state, electrons must have the same spin. This is a fundamental property of quantum mechanics and is governed by the Pauli exclusion principle.
Yes, in certain situations, such as in heavy atoms or molecules with unpaired electrons, the spin of electrons in a triplet state may not be the same. This is due to the influence of external factors, such as the spin-orbit coupling effect.