[QMSE] W01 - Matter | Computer Science

unlike light, the understanding of matter was less advanced in classical physics
strong empirical understanding of much in chemistry and the idea of atoms and elements
- no idea of atom
- why the periodic table is like the way it is

allegedly solves the problem of understand matter
no matter principle can be explained without the paradigm of quantum mechanics
- why a diamond scratches things but pencil lead scratches smoothly, when both are composed of carbon
properties of materials
- conductivity
- transmissivity
- weight
- magnetism
material science, chemistry and many branches of physics rely on quantum mechanics explanation

hydrogen atom spectra

when hydrogen atom is heated up, the spectra only a few lines of emission
- H-delta: 410.2 nm
- H-gamma: 431.4 nm
- H-beta: 486.1 nm
- H-alpha: 656.3 nm
called the balmer series

planetary model of an atom
electrostatic attraction between proton in nucleus and electron in orbit
angular momentum is quantized in terms of plank’s constant \( \frac{h}{2\pi} \)
- \(h\) is the number pulled out of the euro trash’s arse
since this quantization term \( \frac{h}{2\pi} \) occurs so frequently in physics, this is termed \(\bar{h} \)
each orbit is assigned a number \(n\)
the plank’s constant was originally applied to light, but now is applied to explain matter behavior
the spectral lines of hydrogen are the energies of the separations of these different orbitals in energy
jump quantification in hydrogen spectra
- H-delta: 410.2 nm
  - (n = 6 to n = 2)
- H-gamma: 431.4 nm
  - (n = 5 to n = 2)
- H-beta: 486.1 nm
  - (n = 4 to n = 2)
- H-alpha: 656.3 nm
  - (n = 3 to n = 2)
this jump quantification is the basic theory of why materials have the colors that they have
- these energy levels may be calculated
- and the color of a material may be figured out based on their interaction with light
bohr’s model integrated planck’s constant in the theory of matter
- approximates the size of hydrogen atom: \(\frac{1}{10} nm \) diameter
- bohr’s radius: \( 0.5 Å \)
  - Ångström (pronun - “Ong-strum”)

the concept of quantization is valid
- but the angular momentum is not accurate
it predicts the atom would radiate all the time
the atom does not look like a planetary system
- it is not a small point electron in a classical orbit
but the bohr model picture is stuck in everyone heads
- while being only a simplistic, inaccurate model
- possibly because it is the propaganda fed into high school children’s brain when they are extremely impressionable
- and then spend the rest of their lives believing in the wrong things
- and effort has to be put into rewiring their brains for the rest of their lives when they are past their sensitive learning period
as per quantum mechanics models, the orbitals are electron charge density distributions in space

Hydrogen Density Plots

louie de broglie (loo-e de broy) proposed particle with mass also behaves as a wave with wavelength \( \lambda = \frac{h}{p} \)
- \( p \): particle’s momentum
- fits the bohr’s model

werner heisenberg unwittingly reinvented matrices
- with matrix formulations of quantum mechanics
- in 1925 matrices were relatively new

erwin schroedinger’s wave equation
- proposed actual waves for matter
- in the face of it looks more concrete
- it explained the hydrogen atom with the correct orbitals
- the electron charge density functions are from schroedinger’s wave equation

when working with quantum mechanics, we are likely working with matrices or writing schroedinger’s equations in matrix form
after some controversy, schroedinger realized that his and heisenberg’s models were equivalent mathematically
so these two models are the same thing expressed differently
these two models form the basis and core of applications of quantum mechanics in engineering

models and explanations by
- max born
- pascual jordan
- paul dirac
- john von neumann