What is wave-particle duality?
The concept that particles like electrons can exhibit both particle-like and wave-like behavior.
State Heisenberg’s uncertainty principle.
Δx⋅Δp≥ℏ. You cannot precisely know both position and momentum simultaneously.
What is a wavefunction (Ψ)?
Ψ = sin(kx - ωt)
a superposition of waves
A mathematical function that describes the quantum state of a particle, including its probability distribution.
What is superposition in quantum mechanics?
The ability of a quantum system to be in multiple states at once, described by adding wavefunctions.
What is a wavepacket?
corresponding to oscillation of particles,
(google) a group of superposed waves which together form a travelling localized disturbance, especially one described by Schrödinger’s equation and regarded as representing a particle.
Schrödinger equation (time-independent)
use time- indep schrodinger eqn to do ‘mechanics’ w a wavefunc
consider 1D only
consider no additional potentials (free particle, V=0)
placing a particle in a 1D box, what is its V (potential energy)?
V > E
assume Ψ (wavefunc) = 0 for V → ∞
What does “quantization” mean in quantum mechanics?
Physical quantities like energy or angular momentum can only take certain discrete values.
Atomic model for e- is made up of …
F = qE Lorentz Force
V= - ∫F* dr (proportionate to work)
q/ ε = ∫F*dA = E(4πr^2) Gauss Law
E = (1/ 4πε )(q/ r^2) Coulombs Law
What does the Pauli exclusion principle state?
No two fermions can occupy the same quantum numbers, in the same place. Else, Ψt = 0
What are Fermions (Fermi Energy, think of highest energy lvl occupied by e- at absolute 0) vs Bosons?
Fermions: spin half-integer particle, obey Pauli exclusion
S = 1/2, 3/2, 5/2 …
Bosons: spin integer particles, dont obey
S = 1, 2, 3…
What does the double-slit experiment demonstrate?
That electrons produce an interference pattern, proving their wave-like nature.
What is Planck’s constant? (What does it relate?)
the fundamental constant relating energy and frequency.
What is the spin of an electron?
S = 1/2, with projections m = +1/2 or -1/2
How are atomic orbitals filled according to quantum rules?
From lowest to highest energy, obeying the Pauli exclusion principle and Hund’s rule.
eg. [Cu] = 1s2 2s2 2p6 3s2 3p6 3d9 4s2 since 4s energy lvl lower than of 3d
