低速运动的微观粒子的运动规律
希尔伯特空间：波函数，厄米算符
$$ i\hbar\frac{\partial\Psi}{\partial t}=-\frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2}+V\Psi=\hat H\Psi.\\ i\hbar \frac{\partial \left | \psi (x,t) \right \rangle }{\partial t} = \hat H\left | \psi \right \rangle \ \ \&\ \ \hat H\left | \psi \right \rangle =E_{EigenOfH}\left | \psi \right \rangle $$
态叠加原理：$|\psi\rangle =c_1|\psi _1\rangle+c_2|\psi _2\rangle,c_1+c_2=1$
全同性原理 [The Identity of Indiscernibles → Pauli exclusion principle] description in wikipedia
<aside> 🦄 The Postulates by Shankar 1 【量子态】[wave function] The state of the particle is represented by a vector $\ket {\psi(t)}$ in Hilbert space. 2 【观测物理量之间的对应规则】[Obserable - Measure value] The independent variables $x$ and $p$ of classical mechanics are represented by Hermitian operators $\hat x,\hat p$ with the follwing matrix elements in the eigenbasis of $\hat x$: $\bra x\hat x\ket {x^\prime}=x\delta(x-x^\prime)\\\bra x\hat p\ket {x^\prime}=-i\hbar\delta(x-x^\prime)$. The operators corresponding to dependent variables $\omega(x,p)$ are given Herimitian operators $\hat \omega(\hat x,\hat p)=\omega(x\to \hat x,p\to\hat p)$ 3 【测量公设】[Measurement] If the particle is in a state $\ket \psi$, measurment of the variable(corresponding to )$\hat\omega$ will yield one of the eigenvalues $\omega$ with probability $P(\omega)\propto|\bra \omega \psi\rangle|^2$. The state of the system will change from $\ket \psi$ to $\ket \omega$ as a result of the measurement. 4 【运动方程】[$\text{Schrödinger equation}$] The state vector $\ket{\psi(t)}$obeys the $\text{Schrödinger equation}$, where$\hat H\ket{\psi(t)}\to\hat H(\hat x,\hat p)=H(x\to \hat x,p\to \hat p)$ is the quantum operator and $H$ is the Hamiltonian for the corresponding classical problem. 5 【全同粒子公设】[The Identity of Indiscernibles]
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