$ \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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$\mathbb{P}_k=\ket{a_k}\bra{a_k}$ is the projection onto the $k^{\text{th}}$ eigenstate.

Notations

Coming soon

Concepts

If we sum over a complete set of states, then $$\begin{align*} \sum_{k}^{n}\ket{a_k}\bra{a_k}=1 \end{align*}$$
The probability of measuring the state $\ket{a_n}$ can also be written $\text{Prob}(\ket{a_n})=|c_n|^2=\braket{\psi|\mathbb{P}_n|\psi}$
$\mathbb{P}_k=\ket{a_k}\bra{a_k}$ is the projection onto the $k^{\text{th}}$ eigenstate.

Notations

Coming soon

Concepts

If we sum over a complete set of states, then $$\begin{align*} \sum_{k}^{n}\ket{a_k}\bra{a_k}=1 \end{align*}$$
The probability of measuring the state $\ket{a_n}$ can also be written $\text{Prob}(\ket{a_n})=|c_n|^2=\braket{\psi|\mathbb{P}_n|\psi}$
FullPage
Overview
Notations
Concepts
FullPage
Overview
Notations
Concepts
$\mathbb{P}_k=\ket{a_k}\bra{a_k}$ is the projection onto the $k^{\text{th}}$ eigenstate.

Notations

Coming soon

Concepts

If we sum over a complete set of states, then $$\begin{align*} \sum_{k}^{n}\ket{a_k}\bra{a_k}=1 \end{align*}$$
The probability of measuring the state $\ket{a_n}$ can also be written $\text{Prob}(\ket{a_n})=|c_n|^2=\braket{\psi|\mathbb{P}_n|\psi}$
$\mathbb{P}_k=\ket{a_k}\bra{a_k}$ is the projection onto the $k^{\text{th}}$ eigenstate.

Notations

Coming soon

Concepts

If we sum over a complete set of states, then $$\begin{align*} \sum_{k}^{n}\ket{a_k}\bra{a_k}=1 \end{align*}$$
The probability of measuring the state $\ket{a_n}$ can also be written $\text{Prob}(\ket{a_n})=|c_n|^2=\braket{\psi|\mathbb{P}_n|\psi}$
FullPage
Overview
Notations
Concepts