$ \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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Postulate 1

The state of a quantum mechanics system, including all the information that is known about it, is mathematically represented by a normalized vector know as a ket, denoted with $|\psi\rangle$.

Postulate 2

An operator is a mathetmatical object that acts on a ket and transforms it into a new ket.

Postulate 3

The only possible results of a measurement of a observable is one of the eigenvectors of the corresponding operator.

Postulate 4

The probability of observing an eigenvalue (with the associated eigenvector $|\phi\rangle$) in a measurement of an observable on a system in the state $|\psi\rangle$ is $$\begin{align*} P_{\pm}=|\langle \phi | \psi\rangle | ^2 \end{align*}$$

Postulate 5

After a measurement of $A$ that yields the result $a_n$ (one of the eigenvalues) of the quantum state is in $$\begin{align*} |\psi\rangle =\frac{\mathbb{P}_n|\psi\rangle}{\sqrt{\langle \psi|\mathbb{P}_n|\psi\rangle}} \end{align*}$$

Postulate 6

The time evolution of a quantum system is determined by the total energy of the system through the Hamiltonian operator $H(t)$ according to the schrodinger's equation $$\begin{align*} i\hbar\frac{d}{dt}|\psi(t)\rangle = H(t)|\psi(t)\rangle \end{align*}$$

Postulate 1

The state of a quantum mechanics system, including all the information that is known about it, is mathematically represented by a normalized vector know as a ket, denoted with $|\psi\rangle$.

Postulate 2

An operator is a mathetmatical object that acts on a ket and transforms it into a new ket.

Postulate 3

The only possible results of a measurement of a observable is one of the eigenvectors of the corresponding operator.

Postulate 4

The probability of observing an eigenvalue (with the associated eigenvector $|\phi\rangle$) in a measurement of an observable on a system in the state $|\psi\rangle$ is $$\begin{align*} P_{\pm}=|\langle \phi | \psi\rangle | ^2 \end{align*}$$

Postulate 5

After a measurement of $A$ that yields the result $a_n$ (one of the eigenvalues) of the quantum state is in $$\begin{align*} |\psi\rangle =\frac{\mathbb{P}_n|\psi\rangle}{\sqrt{\langle \psi|\mathbb{P}_n|\psi\rangle}} \end{align*}$$

Postulate 6

The time evolution of a quantum system is determined by the total energy of the system through the Hamiltonian operator $H(t)$ according to the schrodinger's equation $$\begin{align*} i\hbar\frac{d}{dt}|\psi(t)\rangle = H(t)|\psi(t)\rangle \end{align*}$$
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FullPage
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5

Postulate 1

The state of a quantum mechanics system, including all the information that is known about it, is mathematically represented by a normalized vector know as a ket, denoted with $|\psi\rangle$.

Postulate 2

An operator is a mathetmatical object that acts on a ket and transforms it into a new ket.

Postulate 3

The only possible results of a measurement of a observable is one of the eigenvectors of the corresponding operator.

Postulate 4

The probability of observing an eigenvalue (with the associated eigenvector $|\phi\rangle$) in a measurement of an observable on a system in the state $|\psi\rangle$ is $$\begin{align*} P_{\pm}=|\langle \phi | \psi\rangle | ^2 \end{align*}$$

Postulate 5

After a measurement of $A$ that yields the result $a_n$ (one of the eigenvalues) of the quantum state is in $$\begin{align*} |\psi\rangle =\frac{\mathbb{P}_n|\psi\rangle}{\sqrt{\langle \psi|\mathbb{P}_n|\psi\rangle}} \end{align*}$$

Postulate 6

The time evolution of a quantum system is determined by the total energy of the system through the Hamiltonian operator $H(t)$ according to the schrodinger's equation $$\begin{align*} i\hbar\frac{d}{dt}|\psi(t)\rangle = H(t)|\psi(t)\rangle \end{align*}$$

Postulate 1

The state of a quantum mechanics system, including all the information that is known about it, is mathematically represented by a normalized vector know as a ket, denoted with $|\psi\rangle$.

Postulate 2

An operator is a mathetmatical object that acts on a ket and transforms it into a new ket.

Postulate 3

The only possible results of a measurement of a observable is one of the eigenvectors of the corresponding operator.

Postulate 4

The probability of observing an eigenvalue (with the associated eigenvector $|\phi\rangle$) in a measurement of an observable on a system in the state $|\psi\rangle$ is $$\begin{align*} P_{\pm}=|\langle \phi | \psi\rangle | ^2 \end{align*}$$

Postulate 5

After a measurement of $A$ that yields the result $a_n$ (one of the eigenvalues) of the quantum state is in $$\begin{align*} |\psi\rangle =\frac{\mathbb{P}_n|\psi\rangle}{\sqrt{\langle \psi|\mathbb{P}_n|\psi\rangle}} \end{align*}$$

Postulate 6

The time evolution of a quantum system is determined by the total energy of the system through the Hamiltonian operator $H(t)$ according to the schrodinger's equation $$\begin{align*} i\hbar\frac{d}{dt}|\psi(t)\rangle = H(t)|\psi(t)\rangle \end{align*}$$
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