Quantum Mechanics Quiz
Questions: 16 · 10 minutes
1. In a double-slit experiment, single particles build an interference pattern when no path information is available. What generally happens if an apparatus reliably determines which slit each particle passes through?
The particles gain enough energy to emit photons
The interference fringes become twice as close together
Each particle passes through neither slit
The interference pattern disappears
2. What does the position–momentum uncertainty principle state?
A quantum state cannot have arbitrarily precise position and momentum simultaneously
Measuring position always permanently stops a particle
A particle cannot have both position and momentum under any circumstances
Position and momentum can both be exact if the measuring equipment is sufficiently advanced
3. Two distant particles are entangled and measured. Which statement best matches standard quantum mechanics?
One observer can choose the other observer’s result and send a controllable message instantly
Each particle carried a fully known classical instruction that explains every possible measurement
Their results can show correlations that cannot be used for faster-than-light communication
The particles must exchange ordinary light signals at the moment of measurement
4. Why does a particle confined in an ideal one-dimensional box not have a zero-energy ground state?
The particle continuously absorbs heat from the walls
A zero-energy constant wavefunction cannot satisfy the box’s boundary conditions as a nonzero state
Every confined particle must move at the speed of light
The Pauli exclusion principle forbids zero energy for every kind of particle
5. What is the main role of the time-dependent Schrödinger equation in nonrelativistic quantum mechanics?
It determines the exact result of every individual measurement in advance
It describes how gravity bends spacetime around a particle
It assigns classical trajectories to electrons inside atoms
It governs how a quantum state evolves with time
6. According to Planck’s relation, what determines the energy of a single photon?
Its frequency, through E = hf
Its speed, through E = mc²
Its brightness, through E = IVt
Its electric charge, through E = qV
7. A delicate quantum superposition interacts uncontrollably with many particles in its environment. What process explains the rapid loss of observable interference between its components?
Quantum teleportation
Decoherence
Nuclear fusion
Stimulated emission
8. What does the Pauli exclusion principle imply for electrons in an atom?
Electrons can occupy only circular paths around the nucleus
Every electron must have a different energy from every other electron
No two electrons can occupy the same complete set of quantum numbers
Electrons are forbidden from entering the atomic nucleus
9. Before a quantum system is measured, what does a superposition represent?
A quantum state formed from a combination of possible basis states
Rapid switching between definite states that are individually observable
Experimental uncertainty caused only by imperfect instruments
A mixture produced whenever two particles have equal mass
10. Ideal linearly polarized light passes through a polarizer whose axis is 45° from the light’s polarization. According to Malus’s law, what fraction of the original intensity is transmitted?
One half
About seven tenths
One quarter
All of it
11. Light shines on a metal, but every photon has energy below the metal’s photoelectric threshold. What happens if the light’s intensity is increased without changing its frequency?
Electrons are emitted with greater kinetic energy
No photoelectrons are emitted in the idealized single-photon picture
Electrons are emitted only after the light becomes classically bright enough
The photons automatically increase their frequency at the surface
12. A particle is tunneling through a rectangular barrier. With its energy unchanged, which modification generally makes tunneling more likely?
Replacing the finite barrier with an infinitely high one
Making the barrier higher and wider
Increasing the particle’s mass while keeping everything else fixed
Making the barrier lower and narrower
13. A particle with less energy than a finite potential barrier is occasionally detected on the other side. Which effect best explains this?
Quantum entanglement
Spontaneous photon creation
Pauli exclusion
Quantum tunneling
14. A particle’s normalized wavefunction assigns a complex amplitude to each possible position. How is the position probability density found?
By taking the wavefunction’s ordinary derivative
By taking the squared magnitude of the wavefunction
By multiplying the wavefunction by the particle’s mass
By using only the wavefunction’s real part
15. An electron is measured to be spin-up along the z-axis. It is immediately measured again along the same axis, with no intervening interaction. What is the ideal prediction?
The second measurement must give spin-down
The second measurement has equal chances of spin-up and spin-down
The second measurement gives spin-up with certainty
The electron has no measurable spin after the first measurement
16. A nonrelativistic particle’s momentum doubles. According to the de Broglie relation λ = h/p, what happens to its wavelength?
It doubles
It is squared
It is halved
It remains unchanged