Modern Physics

Uncertainty Principle

ΔxΔp ≥ (2/ℏ​)

product of change in momentum and position must be less then 2 divided by reduced planks constant

ΔEΔt ≥ (2/ℏ)​

product of change in energy and time must be less then 2 divided by reduced planks constant

Plank’s constant and reduced Plank’s constant

h = 6.62607015×10^-34 J

ℏ = h/2π

2π is introduced as quantum mechanics deals with waves that often require rotations

Epsilon nought

ε₀ = 8.85 × 10^-12F×M^-1

Permittivity of free space

Determines the dielectric value of a true vacuum

It determines how much electric field is permitted in a vacuum

Value is found from 1/(μ₀c²)

Mu nought

μ₀ = 1.25 × 10^-6N×A^-2 = 4π 10^-7H/m

Permeability of free space

Determines the strength of a magnetic field induced by an electric current

Fine structure constant

A dimensionless quantity that relates how strongly two charged particles interact through the electromagnetic force

⁠

London penetration depth

LPD describes how an electric field decays exponetially as it enters a superconductor.

B(x) = B_ie^-x/λ

B is the calculated magnetic field at a point x inside a superconductor

B_i is the external magnetic field right above the surface

λ is the London penetration depth of a superconductor

Only applies to type-1 superconductors

Ginzburg-Landau parameter

Determines type of superconductor

κ = λ_L/ξ = Ginzburg-Landau parameter

ξ is coherence length

If κ is less than 1/√2 the superconductor is type 1, meaning all field is expelled through Meissner effect

If κ is greater 1/√2 the superconductor is type 2, meaning some magnetic field remains in the form of Abrikosov vortices

Phonon

They are quantized lattice vibrations

They carry heat in insulations, determine heat capacity of solids, and allow for cooper pair formation

Magnons

Quantized spin waves in magnetic materials

If spin flips in ferromagnetic materils other spins around tend to align, causing a wave

They explain magnetic specific heat, ferromagnetic resonance, neutron scattering results

Excitons

Excites are bound pairs of an electron and a hole(area in latice that lacks an electron)

Together the hole and electron attract eachother

Can form when electrons are promoted to the conduction band

Polarons

Polaron is an electron and its own lattice distortion

Electrons moving through lattices attract cations, causing the lattice to bend towards the electron

Increases effective mass of the electron as it will drag distortions around it

Plasmons

Quantized oscillations of electron density

Sound wave for electrons

Cooper pairs

Pairs of electrons that are bound together by phonons and lattice vibrations at extremely low temperatures

The addition of electron spins in cooper pairs also allow them to act as bosons(this causes the zero resistance of superconductors)