Momentum

#Physics

Classical

$\displaystyle p=mv$

$\displaystyle \frac{ \mathrm{d}p }{ \mathrm{d}t }=F$

• Newton's 2nd Law

Quantum

Topics

• Momentum Operator
• Relativistic Momentum
• De Broglie Wavelength

$\displaystyle p=\hbar k=\frac{h}{\lambda}$

• $\displaystyle \hbar$ is the reduced Planck constant
• $\displaystyle k$ is the angular wavenumber of the particle

$\displaystyle {\left\langle{p}\right\rangle}_{\Psi}=\int \Psi^{*}(\hat{p}\Psi) , \mathrm{d}x=\bra{\Psi}\hat{p}\ket{\Psi}$

$\displaystyle {\left\langle{p}\right\rangle}=m\frac{ \mathrm{d}{\left\langle{x}\right\rangle} }{ \mathrm{d}t }=-i\hbar \int \left( \Psi^{*}\frac{ \partial \Psi }{ \partial x } \right) , \mathrm{d}x$