de Broglie wavelength de Broglie argued that there was a wavelength that could be written from

Schrödinger equation

a 1 a 0 a 2 a0a

Schrödinger equation

Schrödinger equation electron in free space

Schrödinger equation

element nlms Hydrogen 100+1/2 or -1/2 Helium 100+1/2 & -1/2 Beryllium 200+1/2 & -1/2 Lithium 200+1/2 or -1/2

Heisenberg uncertainty principle

Simple marbles – number of ways of organizing the three balls

Simple marbles – number of ways of organizing 5 balls in 3 pails (microstates)

entropy

Entropy of five marbles in the three pails – 2 & 1 & 2

Two constraints

Calculate the dimensions of a rectangular garden that has a hill that is surrounded by a fence of a fixed length c. (Lagrange multiplier)

entropy

Maxwell Boltzmann distribution

Water bag distribution

Schrödinger equation

12345 Are there electrons in the state? 12345

Fermi-Dirac distribution n j is the number of particles in state j e j is the energy of state j g j is the degeneracy of state j (the number of states with energy e j )  is the chemical potential  B is Boltzmann’s constant T is absolute temperature

Fermi-Dirac distribution