Difference between distinguisable and indistinguisable particle in points
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As the name suggests, distinguishable particles can be distinguished from one another. You can tell which is which particle in this case. They have an individualistic nature. Two particles may be identical yet treated as distinguishable as is done in classical statistical mechanics. Technically, such particles have thermal de Broglie wavelengths much smaller than average interparticle separation. This is what happens in the classical world. Even if you have two identical tennis balls you can physically distinguish. The Maxwell-Boltzmann Statistics works here.
This doesn't hold in quantum mechanics. Two identical particles in quantum mechanics are indistinguishable in the sense that you can't tell which is which. Consider for example, two electrons in the He atom. You can't talk about this electron or that electron. You only talk about an electron. There is no way to distinguish between the two electrons in the 1s orbital. Technically, the de Broglie wavelengths are of the order or larger than interparticle separations. Quantum statistical mechanics works here for counting distributions of systems with indistinguishable particles.
This doesn't hold in quantum mechanics. Two identical particles in quantum mechanics are indistinguishable in the sense that you can't tell which is which. Consider for example, two electrons in the He atom. You can't talk about this electron or that electron. You only talk about an electron. There is no way to distinguish between the two electrons in the 1s orbital. Technically, the de Broglie wavelengths are of the order or larger than interparticle separations. Quantum statistical mechanics works here for counting distributions of systems with indistinguishable particles.
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