Energy conservation as a wave equation

Science · Quantum & Modern Physics · ages 19-20

Name ______________________ Date ____________

The time-independent equation applies when the potential does not change with time.
Circle one: True False
In the Schrodinger equation, what does the curvature term stand for?
- Potential energy
- Total energy
- Kinetic energy
What must psi do at an infinite wall?
- Peak sharply
- Vanish to zero
- Oscillate fastest
One region of psi curves much more sharply than the rest. What is true there?
- Kinetic energy is higher there
- Potential energy is zero there
- Total energy differs there
A well holds whole half-waves. How many half-waves fit the n equals 2 state?
Answer: ______________
What makes a state stationary?
- Its probability density never changes in time
- Its particle sits still at one point
- Its energy keeps drifting
Which candidate is a valid well solution?
- Nonzero at a wall but normalised
- Zero at both walls and normalised
- Infinite inside the well
n equals zero is the ground state of the infinite well.
Circle one: True False

Answer key

For grown-ups. Fold this page away before handing over the rest.

True · A steady potential lets the time part separate off.
Kinetic energy · Curvature of psi plays the kinetic role in the budget.
Vanish to zero · The particle is never beyond the wall, so psi is zero there.
Kinetic energy is higher there · Sharper curvature is more kinetic energy in that region.
2 · The index n counts the fitted half-waves.
Its probability density never changes in time · One fixed energy freezes the shape of the chances.
Zero at both walls and normalised · Valid means meeting the walls and normalisable inside.
False · That solution is zero everywhere and cannot be normalised.