A sharper microscope can prepare a state with ΔxΔp below ħ/2.

Circle one:   True   False

For finite position and momentum standard deviations along one axis, which relation holds?

• ΔxΔp is greater than or equal to ħ/2.
• ΔxΔp is exactly equal to ħ in every state.
• ΔxΔp is less than or equal to ħ/2.

Why does a localised packet involve a spread of possible momenta?

• Its detector always supplies a random heating force.
• Its different wave numbers have different momenta.
• Its position density directly gives its momentum values.

A hypothetical state has a nucleus-sized Δx instead of an atom-sized Δx. What follows from the uncertainty relation?

• Its momentum lower bound becomes much smaller.
• Its momentum lower bound remains unchanged.
• Its momentum lower bound becomes much larger.

Use ħ = 1.056e-34 J s. If Δx = 2.00e-10 m, the momentum lower bound is a × 10^-25 kg m/s. What is a?

Answer: ______________

A state has ΔxΔp = 0.80ħ. Which conclusion follows from the position-momentum uncertainty relation?

• It must be a minimum-product state.
• It satisfies the stated lower bound.
• It must violate the stated lower bound.

Δx is halved. What is the new momentum lower bound divided by the old momentum lower bound?

Answer: ______________

Let L > 0. State A has Δx = 4L and Δp = ħ/L. State B has Δx = 2L and Δp = ħ/(2L). Because both spreads shrink, B violates ΔxΔp ≥ ħ/2.

Circle one:   True   False