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Diffstat (limited to 'latex/know/concept/pauli-exclusion-principle/source.md')
| -rw-r--r-- | latex/know/concept/pauli-exclusion-principle/source.md | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/latex/know/concept/pauli-exclusion-principle/source.md b/latex/know/concept/pauli-exclusion-principle/source.md index d1c2149..f95541f 100644 --- a/latex/know/concept/pauli-exclusion-principle/source.md +++ b/latex/know/concept/pauli-exclusion-principle/source.md @@ -3,8 +3,8 @@ # Pauli exclusion principle -In quantum mechanics, the **Pauli exclusion principle** is a theorem that -has profound consequences for how the world works. +In quantum mechanics, the **Pauli exclusion principle** is a theorem with +profound consequences for how the world works. Suppose we have a composite state $\ket*{x_1}\ket*{x_2} = \ket*{x_1} \otimes \ket*{x_2}$, where the two @@ -34,8 +34,8 @@ $$\begin{aligned} As it turns out, in nature, each class of particle has a single associated permutation eigenvalue $\lambda$, or in other words: whether -$\lambda$ is $-1$ or $1$ depends on the species of particle that $x_1$ -and $x_2$ represent. Particles with $\lambda = -1$ are called +$\lambda$ is $-1$ or $1$ depends on the type of particle that $x_1$ +and $x_2$ are. Particles with $\lambda = -1$ are called **fermions**, and those with $\lambda = 1$ are known as **bosons**. We define $\hat{P}_f$ with $\lambda = -1$ and $\hat{P}_b$ with $\lambda = 1$, such that: @@ -109,7 +109,7 @@ $$\begin{aligned} = 0 \end{aligned}$$ -At last, this is the Pauli exclusion principle: **fermions may never +And this is the Pauli exclusion principle: **fermions may never occupy the same quantum state**. One of the many notable consequences of this is that the shells of atoms only fit a limited number of electrons (which are fermions), since each must have a different quantum number. |