Where ψ = 2i, the probability density |ψ|² equals 4.

What is the normalisation condition?

• The integral of ψ itself over space equals one
• The integral of |ψ|² over space equals one
• The value of ψ at every position equals one

Using dimensionless x, ψ = 1/√10 on [0, 10] and zero elsewhere. What is P(0 < X < 3)?

• 0.03
• 3.00
• 0.30

For a normalised one-dimensional state with finite position expectation, how is E[X] computed?

• Integrate x times |ψ|² over its range
• Integrate x times ψ over its full range
• Choose the position of the highest density

Using dimensionless x, ψ(x) = 3C on [0, 1], 4C on (1, 2], and zero elsewhere. What positive real C normalises ψ?

A normalised position density is even about zero, and ∫ |x|ρ(x) dx is finite. What is E[X]?

• Zero, from cancelling contributions
• The largest positive position allowed
• The distance between the two outer peaks

Using dimensionless position x, a normalised wavefunction is ψ(x) = √(3/8)x on [0, 2] and zero elsewhere. Find the expectation of position.

A student says the average position must be a spot where the particle can be found.