Quantum Flashcards
What prediction did classical physics make about the emittance of a body?
an ultraviolet catastrophe
What is a photon?
- a packet or ‘chunk’ of radiation energy - NOT a particle
- a probability wave
Equations for the photoelectric effect?
E{photon} = W + KE = W + eV
W = hf where f = threshold frequency at V = 0
KE{max} = eV{o} where V{o} = stopping voltageWhat predictions were made of the photoelectric effect?
What observations were made?
Predicted (classical physics) as intensity increases:
- more electrons emitted
- KE of electrons increases, so higher stopping voltage
- no dependence on frequency
- there will be a time delay
Observed as intensity increased:
- more electrons emitted
- no change to stopping voltage > KE did not increase
- no time delay
- dependence on frequency
What is Einstein’s postulate?
energy in the field itself is quantised into amounts hf as if made up of particles – photons
What are two types of X-ray produced and how are they produced?
- Brehmsstrahlung radiation (‘braking’ radiation): electron loses energy when interacting with nuclei, slows down and emits a photon
- Characteristic radiation: incoming electron strikes subshell electron, the subshell electron gains energy, and when it de-excites, releases a photon of characteristic energy
What does a X-ray diagram look like? (incl. axes & labels, cut-off points)
- y-axis: X-ray intensity
- x-axis: wavelength
- brehmsstrahlung curve
- some characteristic peaks
- cut-off point minimum wavelength/maximum photoenergy
What fact and equation did the Compton effect prove?
That photons have momentum, p = h/λ{de broglie}
What was puzzling about the results of the Compton experiment?
At different angles, a second peak appeared: the constant peak was caused by strongly-bound electrons not causing a scattering effect; the second peak caused by a difference in wavelength
What is the equation for the Compton effect?
λ{f} - λ{i} = h/mc * (1 - cosθ), where θ = angle of scattering
When is the Compton effect greatest?
When θ = 180 deg / π rad
What is the de Broglie wavelength?
The natural wavelength of all quantum particles
What experiment confirmed de Broglie’s theory on the wave nature of quantum particles?
Bragg Scattering, showed electron diffraction
What is the equation for the Bragg Scattering? Where does the maximum occur?
2dsinθ = n*λ, maximum at 2d = λ
What is the Heisenberg Uncertainty Principle?
Position and momentum are ‘incompatible observables’: Δp * Δx > [h bar]/2
The square of the absolute value of the wavefunction is proportional to…
… the probability density of finding a ‘particle’ in a small region around position x.
What does the Schrodinger Equation mean?
It shows that the probability of finding a particle in some dx is ABSOLUTELY UNIFORM. At any time, until a measurement is made, the position of the particle is entirely unknown.
When a measurement is taken, quantum probability becomes certainty. This is known as…
Quantum decoherence.
What are the Bohr postulates?
- electrons in an atom move in circular orbit, and the angular momentum l is quantized: l = mvr = n*[h bar]
- an electron in one of these orbits is stable, but if it
discontinuously changes its orbit, energy is emitted or
absorbed in photons satisfying: ΔE = hf = [h bar]*ω
What are the values for the Bohr radius and 1 Rydberg?
Bohr radius a{o} = 0.0529 nm
1 Rydberg = 13.6 eV
What are the formulae for r and E in Hydrogen-like atoms?
r = (n^2 / Z) a{o}
E = - (Z/n)^2 RyState the successes and failures of the Bohr model of the atom.
Successes: - explained stable atoms - quantised energy levels - emission/absorption spectra of H Drawback: - fails in detail for atoms other than H - l = 0 was omitted
How do we improve the Bohr atom model?
- reduced mass = mM / (m + M)
- altered Rydberg constant: R/R{infinity} = 1 / (m/M +1)
Which correction included the “fine structure” of atoms and atomic orbitals?
Bohr-Sommerfeld correction
How many different orientations can a photon have and what are they?
Four: Horizontal, Vertical, +/- 45 deg
+ and x photon orientations are…
… incompatible observables.
Measurements in quantum are…
… probabilistic, instead of deterministic.
In quantum cryptography, if a message is read by a hacker, what proportion of the signal that is returned to the original recipient carries errors?
1/4th of the message is erroneous.
What crystal is used to polarise light?
Birefringent crystals.
What is the difference between the classical and quantum polarisations of 45 degree-oriented light through a H/V crystal?
- classically, 50% of the light will take a H-path, and the other 50% will take the V-path
- in quantum measurements, this becomes a probability: 50% probability of photon taking H-path, and 50% probability of photon taking V-path.
A photon in an H or V state, going through a H/V crystal, is in an [blank] of the measurement operator.
Eigenstate.
What is the name of the operator that changes the polarisation of light?
Pockels cell.
What causes the quantisation of energy?
The confinement of waves (matter or probability waves) in a potential well.
What is the expression that defines the length of any potential well, or the waves confined in it?
Each potential well must have a length of integer 0.5 de Broglie wavelengths. L = n * 0.5 * λ{dB}
What is the equation of a wavefunction in an infinite potential well?
Ψ = sqrt(2/L) * sin(nπx/L)
What is the relativistic kinetic energy of a particle?
KE = sqrt(p^2c^2 + m^2c^4)
True or false: the probability equation for finding a quantum particle in an infinite well has an oscillating part only.
False.
True or false: superposition of wavefunctions works on the same principle as classical waves.
False.
What are the two possible approaches to quantum computing?
Superposition of wavefunctions, and quantum entanglement.
If two wavefunctions interfere destructively, what is the probability compared to the classical probability?
If from the wavefunction p(x) < p{cl}, the probability amplitudes interfere destructively.
