# LaTeX

## Contents

- 1 Energy levels for particle in 1-D box
- 2 Relativistic energy
- 3 One-dimensional Schrödinger wave equation
- 4 Magnetic field around a single wire
- 5 Probability of finding an object on the other side of a quantum barrier
- 6 Uncertainty in energy of a state with lifetime
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau\ }** - 7 Van Der Waals Gas
- 8 Diffraction Experiment
- 9 Eyring constant
- 10 Difference Map
- 11 Quadratic formula
- 12 Arithmetic mean
- 13 Geometric mean
- 14 Mexican Hat

## Energy levels for particle in 1-D box

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E = \frac {\pi^2 \hbar^2 n^2} {2 m a^2}}**

Where n is an integer, **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n= 1,2,3,\dots}**

and **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \hbar = \frac h {2 \pi} }**

so **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E = \frac {\pi^2 h^2 n^2} {2 m a^2 4 \pi^2} = \frac {h^2 n^2} { 8 m a^2} }**

## Relativistic energy

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \ {E^2=p^2 c^2 + m_0^2 c^4} }**

## One-dimensional Schrödinger wave equation

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle - \frac {\hbar^2} {2m} \frac {d^2 \psi (x)} {dx^2} + U(x)\psi(x) = E\psi(x)}**

## Magnetic field around a single wire

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r = \frac {\mu _{0}I} {2 \pi B} }**

## Probability of finding an object on the other side of a quantum barrier

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P = \exp \left( -2d \sqrt { \frac {2m(V-E)} { \hbar^2} } \right) }**

## Uncertainty in energy of a state with lifetime **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau\ }**

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\delta}E = \frac h {2 \pi\ } \tau\ }**

## Van Der Waals Gas

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left ( p + \frac {an^2} {V^2} \right ) (V - nb) = nRT}**

## Diffraction Experiment

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(hkl) = \sum _{j} f _j (\theta) \cdot \exp[-8\pi^2U_j\sin^2 \frac {\theta} {\lambda^2}] \cdot \exp [2 \pi i (hx_j + ky_j + i z_j]}**

## Eyring constant

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k= \frac {k_B T} n k^ \ddagger\ }**

## Difference Map

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta \rho (xyz) = \frac 1 {V} \sum _{hkl} ( \left| F _{obs} \right| - \left| F_{calc} \right|) \exp[-2 \pi i(hx+hy+lz-\alpha _{hkl})] }**

## Quadratic formula

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_{0,1} = \frac {-b \pm \sqrt { b^2 - 4ac } } {2a}}**

## Arithmetic mean

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r = \frac {1} {N} \sum_{n=1}^N r_n }**

## Geometric mean

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r = [ ( 1 + r_1 ) ( 1 + r_2 ) \dots ( 1 + r_N ) ] ^\frac { 1 } { N } - 1 }**

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r = (\sum_{n=1}^N 1 + r_n)^\frac {1}{N} - 1 }**

## Mexican Hat

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \psi(t) = {2 \over {\sqrt {3\sigma}\pi^{1 \over 4}}} \left( 1 - {t^2 \over \sigma^2} \right) e^{-t^2 \over 2\sigma^2}}**