Momentum

Classical

$p=mv$

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

• Newton’s 2nd Law

Quantum

Topics

• Momentum Operator
• Relativistic Momentum
• De Broglie Wavelength

$p=\hslash k=\frac{h}{\lambda }$

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

${⟨p⟩}_{\Psi }=\int {\Psi }^{\ast }(\hat{p}\Psi )\mathrm{d}x=⟨\Psi |\hat{p}|\Psi ⟩$

$⟨p⟩=m\frac{\mathrm{d}⟨x⟩}{\mathrm{d}t}=-i\hslash \int \left({\Psi }^{\ast }\frac{\partial \Psi }{\partial x}\right)\mathrm{d}x$