The Uncertainty Principle Equation Formula Latex Code and Summary

The Uncertainty Principle

Tags: #physics #quantum

Equation

$$(\Delta A)^2=\left\langle \psi|A_{\rm op}-\left\langle A \right\rangle|^2\psi \right\rangle=\left\langle A^2 \right\rangle-\left\langle A \right\rangle^2 \\ \Delta A\cdot\Delta B\geq \frac{1}{2} |\left\langle \psi|[A,B]|\psi \right\rangle| \\ \Delta E\cdot\Delta t\geq\hbar \\ \Delta p_x\cdot\Delta x\geq \frac{1}{2} \hbar \\ \Delta L_x\cdot\Delta L_y\geq \frac{1}{2} \hbar L_z$$

Latex Code

                                 (\Delta A)^2=\left\langle \psi|A_{\rm op}-\left\langle A \right\rangle|^2\psi \right\rangle=\left\langle A^2 \right\rangle-\left\langle A \right\rangle^2 \\
             \Delta A\cdot\Delta B\geq \frac{1}{2} |\left\langle \psi|[A,B]|\psi \right\rangle| \\ 
             \Delta E\cdot\Delta t\geq\hbar \\ 
             \Delta p_x\cdot\Delta x\geq \frac{1}{2} \hbar \\ 
             \Delta L_x\cdot\Delta L_y\geq \frac{1}{2} \hbar L_z

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Introduction

$(\Delta A)^2=\left\langle \psi|A_{\rm op}-\left\langle A \right\rangle|^2\psi \right\rangle=\left\langle A^2 \right\rangle-\left\langle A \right\rangle^2 \\ \Delta A\cdot\Delta B\geq \frac{1}{2} |\left\langle \psi|[A,B]|\psi \right\rangle| \\ \Delta E\cdot\Delta t\geq\hbar \\ \Delta p_x\cdot\Delta x\geq \frac{1}{2} \hbar \\ \Delta L_x\cdot\Delta L_y\geq \frac{1}{2} \hbar L_z$

Latex Code

            (\Delta A)^2=\left\langle \psi|A_{\rm op}-\left\langle A \right\rangle|^2\psi \right\rangle=\left\langle A^2 \right\rangle-\left\langle A \right\rangle^2 \\
             \Delta A\cdot\Delta B\geq \frac{1}{2} |\left\langle \psi|[A,B]|\psi \right\rangle| \\ 
             \Delta E\cdot\Delta t\geq\hbar \\ 
             \Delta p_x\cdot\Delta x\geq \frac{1}{2} \hbar \\ 
             \Delta L_x\cdot\Delta L_y\geq \frac{1}{2} \hbar L_z

Explanation

Latex code for The Uncertainty Principle. I will briefly introduce the notations in this formulation.

$\Delta A$ : Uncertainty in A

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