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Big 3 Fundamental Discoveries

1. Electron energies are quantized (blackbody radiation)
2. Light energy is quantized (photoelectric)
3. H atom quantized (Rydberg Atomic Model)


Bohr's (Guessing) Model

overall, electron radii quantized
1. Electron travels in circular orbit around atom (false, would radiate EMF)
2. Electron doesn't radiate EMF (pussy answer)
3. Orbital Angular Momentum (L) is quantized

Incorrect prediction, but quantized electron values for H atom is correct and idea that L is quantized also correct, and at least he tried


Correspondence Principle

Domain ~ dB wavelength -- quantum; energy gaps for electron will be in distinct levels, so only certain E's apply

Domain too far from dB wavelength --> classical, any E is fine


Uncertainty Principle

x*p or e*t --> hbar/2 --> h/(4pi); derived from Heisenberg

Can't know these two variables at same time with precision because of wave-particle duality --> our measurements would affect the other


Schrodinger Eqn

^H * psi = ^E * psi
allows us to find wave functions and E for an electron in ANY domain
"Energy of particle (kinetic, potential, etc) times wave function equals overall energy of particle times wave function"


Probability amplitude

the complex conjugate of our wavefunction (to eliminate imaginary values)


Square modulus

"Square" --> our wavefunction multiplied by complex conjugate
"Modulus" --> absolute value
Represents the likelihood of finding something --> the probability density
Probability density = Square modulus; two interpretations:
1. likelihood of finding object within given region of space (particle)
2. fraction of object's properties that will be found in given region of space (wave)

**Classical and quantum data derived from this (amplitude and wave function gives us electron density and charge + mass density, respectively)


Is my wave function okay?

Idk is she:
1. single valued
2. normalized (finite)
3. continuous within our interval
4. has a 1st derivative that's continuous
5. satisfies her boundary conditions with the wave function


Rules for QM operators

1. has corresponding classical mech variable (ie: ^K and K)
2. obey operator algebra
3. Obey the Quantum Average Value Theorem
4. Eigenfunctions of same wavefunction are ORTHOGONAL to each other
5. Eigenfunctions of 2 QM operators will obey Uncertainty Principle if they don't commute


Average/Expectation value
Essentially what would we expect to get in real world setting
Squared modulus with operator in between psi and psi* for integral
for an operator that corresponds to physically measurable value, the average value is denoted as "real world" operator (ie: ^A is our operator, we would put in little a in equation)