Quantum mechanics Flashcards
(44 cards)
4 evidence of energy quantisation
- photoelectric effect
- atomic spectra
- temperature dependency of Cv
- Black body radiation
How can black body radiation show energy quantisation
- blackbody heats up
- charged e- vibrate and emit EM waves
Classicial : Energy is inifinite at short wavelength
Quantum : Photons with high frequency requires large energy jumps so rare at low temperatures
4 Condition for schrodinger eq.
- continuous
- finite value
- differentiable (1st and 2nd derivative exists)
- single-valued in each position
what are the components that makes up the schrodinger eq.
How to form the probability density function from a wavefunction?
What are the 5 applications of the schrodinger eq.
- free particle
- 1D box
- harmonic oscillator
- rotations
- particle of a sphere
- electronic transition
Steps to solve** free particle**
- Define the wavefunction
- find the derivatives of ψ
- no potential component
to find k
conclusion: energy is not quantised
Explain the hisenburg principal
and
when it’s applicable
- delta = uncertainty
- if we know λ = uncertainty in displacement is inf.
- if particle is localised -> ψ = 0 except at position
- Therefore cannot have a momentum=0
Steps to solve
1D box
- Potential at 0 and L = inf.
- find λ - depend on energy level n
Energy - use energy, momentum relations + De Broglie λ
Amplitude - solve for ψ + find pre-factor
Analogy to solve
Harmonic oscillator
Analogy : EPE of spring + SHM
- V = 1/2kx^2
- x=Asin(ωt+ϕ)
- F=−kx
2 components of the wavefunction for
Harmonic oscillator
Hv = Hermite’s polynomial
ξ = dimensionless displacment
How to find
ξ = dimensionless displacment
where ξ is just the displacement ratio and alpha = the overall length
How to convert a 2 body oscillation problem
reduced mass
how to find Energy of
harmonic oscillator
- find the frq. of oscillation
- then find energy
(both eq. given in formula booklet)
+ just need spring constant, mass
3 quantum numbers involved in rotations
and
what they quantise
- n = principal quantum number = energy level
- l = angular momentum = component of anugular momentum in z-dimension
- mL = magnetic quantum no. - orbital orientation (depend on l)
What values are possible for l, angular momentum number
l = 0,1,2,3, …. , n-1
How to find mL, magnetic quantum number
from l, angular momentum
mL = -L ,-L+1, -L+2 …… 0 ……. L-2, L-1, L
e.g. for
find the set of magnetic quantum number for 3d orbital
(deduce from the quantum no. -> atimuthal -> magnetic )
- n = 3
- L = 0,1,2 (n-1)
mL = -2,-1,0,1,2
What does J and Jz actually mean
- J is the angular momentum of the rotation
- Jz is the z-component of the angular momentum
How do I solve for the wavelength of the 2D rigid rotator
constructive interference - circumference = integer no. of λ
Solve for the energy of the 2D rigid rotator
- constructive interference boundary condition
- De Brogile λ
- momentum -> energy conversion
What kind of problem is the hydrogen atom?
Two body problem between nucleus and electron
(use reduced mass)
2 key difference about the hydrogen atom
compared to other schrodinger solutions
- 2 body (reduced mass)
- present of potential (use columbs law)
What is the RDF used for
Probability density of finding a particle at a distance r from a reference particle
integrate to find probability
or find m = 0 for max probability
