quantum-mechanics pauli-exclusion-principle

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edited Apr 25 "12 at 15:07

Qmechanic♦

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asked Apr 25 "12 in ~ 14:43

user8791user8791

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1) Quantum mechanical waves room probability waves, i.e.

*the probability*of detect a particle has a functional dependence top top sines and also cosines. It has nothing to execute with amplitude as power or inert or whatever, the crescents and troughs are increased and also decreased probabilities that being found when an monitoring is made.

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2)Particles have actually spins. Corpuscle that have actually integer turn are referred to as bosons and *can* occupy the same room at the very same time definition the probability of recognize one in one (x,y,z) coordinate boosts the more of them over there are. Bosons can occupy the very same quantum state in general. Particles with fifty percent integer spin are fermions and also follow the fermi-dirac statistics , and also thus cannot occupy the same space; i.e the probability of detect one in one (x,y,z) point out will constantly be the probability for finding one particle; only one deserve to occupy a quantum state in ~ a time, in general.

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answered Apr 25 "12 at 15:26

anna vanna v

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$egingroup$ Thanks. In an answer to your 1st point- what around electrons? they aren't particles-they're literally waves in the quantum field. As such why can't they exist in the same place at the exact same time? $endgroup$

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Apr 25 "12 in ~ 16:15

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Particles room not waves, or at least not in the sense of water waves or electromagnetic waves. It"s true the particles are described by a wavefunction, but in general the wavefunction is a complicated function of plenty of variables. The an easy solutions to Schrodinger"s equation that you learn in primary school QM classes tend to it is in waves, but these are special cases and also not typical of the actual world.

If you take two particles, e.g. Two electrons, then you can"t simply take separate wavefunctions because that each bit and add them, as you would v e.g. Water waves. This is since the electrons interact and this interaction introduces a brand-new term come the potential power term in the Schrodinger equation. This means you have actually to describe the 2 particle mechanism by a new wavefunction the is not merely the sum of the two initial wavefunctions.

There is one elementary proof that 2 electrons can"t occupy exactly the exact same quantum state. If you resolve the Dirac equation (it needs to be the Dirac equation due to the fact that the Schrodinger equation doesn"t define spin) you find the result wavefunction is antisymmetric through respect to exchange the the 2 electrons i.e.

$$Psi(e_1, e_2) = - Psi(e_2, e_1)$$

where the adjust $(e_1, e_2)$ come $(e_2, e_1)$ is claimed to indicate we"ve swapped the two electrons. Currently suppose the two electrons space in the same states, that way there is no difference between $e_1$ and $e_2$ i.e.

$$Psi(e_1, e_2) = Psi(e_2, e_1)$$

Combining these equations us get:

$$Psi(e_1, e_2) = - Psi(e_1, e_2)$$

and the only method this have the right to be correct is if $Psi$ is zero once $e_1$ and $e_2$ are the same, i.e. The probability the the two electrons can be in similar states is zero.

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As Anna mentions, not all particles space fermions. Particles v zero rotate are explained by a different equation, the Klein Gordon equation, and they deserve to occupy similar states. In fact this is the beginning of Bose Einstein condensation.