$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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A state of a quantum system is....

Notations

A general state is often denoted with $|\psi\rangle$. If a second state is considered, it may be denoted with $|\phi\rangle$.

Concepts

All general states can be represented in terms of the eigenvector basis of the operator used to measure it.
Let $A$ be an operator used to measure the state $|\psi\rangle$, with the associated eigenvalues $a_i$ and eigenvectors $|a_i\rangle$. Then $$\begin{align*} |\psi\rangle=\sum_{i=1}^n a_i\a_i\rangle \end{align*}$$ for any general state $|\psi \rangle$.
A state of a quantum system is....

Notations

A general state is often denoted with $|\psi\rangle$. If a second state is considered, it may be denoted with $|\phi\rangle$.

Concepts

All general states can be represented in terms of the eigenvector basis of the operator used to measure it.
Let $A$ be an operator used to measure the state $|\psi\rangle$, with the associated eigenvalues $a_i$ and eigenvectors $|a_i\rangle$. Then $$\begin{align*} |\psi\rangle=\sum_{i=1}^n a_i\a_i\rangle \end{align*}$$ for any general state $|\psi \rangle$.
FullPage
Overview
Notations
Concepts
FullPage
Overview
Notations
Concepts
A state of a quantum system is....

Notations

A general state is often denoted with $|\psi\rangle$. If a second state is considered, it may be denoted with $|\phi\rangle$.

Concepts

All general states can be represented in terms of the eigenvector basis of the operator used to measure it.
Let $A$ be an operator used to measure the state $|\psi\rangle$, with the associated eigenvalues $a_i$ and eigenvectors $|a_i\rangle$. Then $$\begin{align*} |\psi\rangle=\sum_{i=1}^n a_i\a_i\rangle \end{align*}$$ for any general state $|\psi \rangle$.
A state of a quantum system is....

Notations

A general state is often denoted with $|\psi\rangle$. If a second state is considered, it may be denoted with $|\phi\rangle$.

Concepts

All general states can be represented in terms of the eigenvector basis of the operator used to measure it.
Let $A$ be an operator used to measure the state $|\psi\rangle$, with the associated eigenvalues $a_i$ and eigenvectors $|a_i\rangle$. Then $$\begin{align*} |\psi\rangle=\sum_{i=1}^n a_i\a_i\rangle \end{align*}$$ for any general state $|\psi \rangle$.
FullPage
Overview
Notations
Concepts