What histories enter the position-space path integral with fixed endpoint positions and times?

• All admissible histories joining the fixed positions and times
• Only stationary histories joining the fixed positions and times
• Only paths of minimum action joining those fixed endpoints

For real action S, which phase factor appears in the real-time path integral?

• exp(-S/ℏ)
• exp(iS/h)
• exp(iS/ℏ)

At one screen point, coherent slit amplitudes 5b and -5b give an ideal dark fringe because their sum is zero.

At a screen point, two coherent slit amplitudes are 3a and -a, with a nonzero. What is their sum?

• 4a; add magnitudes despite the opposite phases
• 2a; add amplitudes with their relative minus sign
• 0; opposite phases cancel unequal magnitudes

Under suitable semiclassical conditions, why can a neighborhood of a stationary-action path give a leading contribution?

• Nearby phases agree to first order around stationary action
• The action is zero along every stationary classical path
• The spatial route is shortest for every stationary path

For E<V in part of a finite static barrier, how does tunnelling fit the path-integral account?

• Transmission requires each history to borrow energy
• Transmission excludes histories crossing the barrier
• Transmission can be nonzero in the full propagator

In the model λ=fT, keep f fixed and increase transmission T from 0.01 to 0.02. What happens to decay rate λ and half-life ln(2)/λ?

• The rate doubles; the half-life halves
• The rate halves; the half-life doubles
• The rate doubles; the half-life doubles

Which situation can require more care than an approximation based on one isolated classical path?

• A large action makes one path exact
• Several stationary paths contribute
• Two stationary paths make K undefined