What does it mean for psi to be an eigenstate of an operator?

• Same shape back, scaled
• The wavefunction vanishes everywhere
• Any function qualifies for any operator

What does the position operator do to a wavefunction?

• Takes a time derivative
• Squares the wavefunction
• Multiplies by x

Measuring a superposition returns the average of the eigenvalues as the single result.

Circle one:   True   False

A state is a 50/50 superposition of E1 and E2. What does one energy measurement give?

• The average of E1 and E2
• Both values at once
• E1 or E2, at random

Applying H to psi returns 3 eV times psi. What do you conclude?

• psi is not an energy eigenstate
• Eigenstate, eigenvalue 3 eV
• The energy averages to 1.5 eV

What action represents the momentum operator?

• A space derivative
• Multiplication by time
• Division by the energy

A student measures E1 once on a superposition and concludes it was an E1 eigenstate all along. What is the error?

• The detector must be broken
• Superpositions always collapse to E1
• One trial proves nothing

Why can position and momentum not both be sharp at once?

• Detectors are too clumsy
• They share no eigenstate
• They cancel each other out