Ch 2: Quantum Mechanics

what are electron spatial length scales

electron confinement smaller than their natural wavelengths, used to see quantum phenomena

what is the photoelectric effect and what does it prove

1. shine light onto metal

2. collector measures emitted electron current

3. stop flow of electrons using stopping voltage

4. measure kinetic energy

outcome: to observe current, you need a specific kinetic energy = threshold energy of knocking out electrons

proves: light consists of particles called photons (discrete, quantized)

what is Φ for electrons?

minimum energy needed to eject electron out of the metal

equation for maximum kinetic energy of emitted electron?

KEmax = hv - Φ

what is the davisson germer experiment and what did it prove

1. direct an electron beam at a sample of nickel

2. collect the electrons scattered off the nickel target

outcome: @ fixed voltage, the intensity of the scattered beam peaks at specific angles, @ fixed angle, the intensity of the scattered beam depends on the voltage

prove: particles can act as waves

debroglie wavelength: a particle w/ momentum magnitude p has wavelength λ

how do wavelength and kinetic energy depend on each other?

λ ∝ (KE)^(-1/2)

equation for kinetic energy of electron

KE = p²/2m

what is w + equation

temporal angular frequency, w = 2pi/Tperiod [rad/s]

what is λ

wavelength, spatial period of a wave, periodicity in space [m]

what is k

wave number, spatial frequency [rad/m]

what is p?

electron momentum [kg*m/s]

how can electrons act as particles and as waves?

solid particles: localized in one spot

waves: spread out

what is a wavepacket

• spatially localized function (particle)

• small pulse/packet made from a summation of sines and cosine over a range of spatial frequencies k

what is the position momentum uncertainty principle

to find where a particle is precisely (small ∆x) → need many wavelengths (big ∆k or ∆p), momentum (∆p) becomes uncertain

what is the time energy uncertainty principle

if the wave peaks in a short amount of time (small ∆t), its energy (∆E) becomes uncertain

what is a wavefunction

used to describe a particle ψ(x,y,z,t)

what does schrodinger’s wave equation do?

describe the spatial (over space) and temporal (over time) evolution (change) of the wavefunction

what does the hamiltonian do

finds total energy

what is an eigenfunction

u(x,t), wave function representing stable state of system

what is an eigenvalue

E, exact definite energy of state

what is the eigenstate

ψ(x), eigenfunction for the TISE (time independent schrodiner equation, TISE)

what is tunnelling

for finite width barriers, transmission probability is non zero (goes through barrier quickly)

how do we get the quantum numbers?

solving TISE in 3d spherical coordinates

what are the quantum numbers

1. principal (n = 1,2,3,…): electron shell and energy level

2. azimuthal (l = 0,1,..,n-1): orbital angular momentum (spdf orbtials)

3. magnetic (m = -l, …, +l): projection on an axis

4. spin (ms = +1/2 or -1/2): spin of electron

what is the pauli exclusion principle

no two electrons in an atom occupy the same quantum state