Wave-Particle Duality and the Birth of Modern Physics
In the photoelectric effect experiment, which property of an incoming photon must have at least a minimum value in order for an electron to be ejected?
Frequency
Particles whose x-spin is measured to be '+x' are sent through an SGz box, and the particles that are measured to be '+z' are sent into an SGx box. What fraction of the original '+x' particles will be found to be '-x'?
25%
What is the key feature of two particles in an entangled spin state?
Exact correlation between measurement outcomes
In what basis must a state be expressed in order to apply the time evolution rule?
Energy eigenstate basis
What shape is the minimum uncertainty wavefunction?
Gaussian
What feature of atomic emission spectra suggests the need for a new type of physics?
Discrete spectral lines
Particles whose x-spin is measured to be '+x' are sent through an SGz box, and the particles that emerge from both outputs are sent (without measuring their spin) into an SGx box. What fraction of the original '+x' particles will be found to be '-x'?
0%
In quantum cryptography, what is the expected 'error rate' if someone is eavesdropping?
25%
What probabilities do NOT change as a particle state evolves through time?
The likelihood of being in a particular energy eigenstate
What can you multiply a wavefunction by without changing the physical state of a particle?
An overall phase
Provide two rationale for thinking of light as a wave.
Double-slit interference pattern, Electromagnetic wave theory
Who invented 'bra-ket' notation?
Paul Dirac
How did Bell's theorem resolve the EPR paradox?
Proved hidden variable theories did not match experimental observations, while QM did
The time evolution of a quantum state proceeds smoothly according to the Schrodinger equation, except at one moment. What moment is that?
The moment of collapse (measurement)
Given a particular wavefunction, what does one do to calculate the likelihood of finding a particle at a particular position?
The likelihood is the value of |psi|^2 at that location
Provide two rationale for thinking of light as a particle.
Discrete dots on a screen in double-slit experiments, Photoelectric effect, etc.
What is one calculating when taking the inner product of a state with another state in quantum mechanics?
The likelihood that the current 'ket' state will be measured to be in the 'bra' state
Why does quantum entanglement not violate causality?
Because you can't control the measurement outcomes to begin with
Why are neutrino flavors not stable over time?
Because they are superpositions of energy eigenstates, not energy eigenstates themselves
What does it mean to 'normalize' the wavefunction?
Multiply psi by an overall value such that the likelihood of getting *some* outcome is 1.
What is the 'ultraviolet catastrophe' and how was it resolved by Max Planck?
Emission energy of blackbodies should go to infinity at high frequency end of the spectrum; resolved by discretizing the light in photons
What is meant by the 'expectational value' of a measured quantity?
The weighted average of all possible measurement values (each is weighted by the likelihood of getting that value)
Name two practical applications of quantum entanglement.
Quantum computing, Cryptography
How does the time evolution rule help explain the double-slit interference pattern?
Phases going through each slit evolve for different amounts of time before reaching a point on the screen
What does it mean for two observables to be 'incompatible'?
Knowing one exactly makes the other completely unknown.