Wavefunctions

Definition

Wavefunctions describe the quantum state of a particle and contain all the information about that particle's position and momentum. They are solutions to the Schrödinger equation and are usually represented by the Greek letter psi ($\psi$).

5 Must Know Facts For Your Next Test

1. Wavefunctions can be used to calculate the probability density of finding a particle in a given region of space.
2. The square of the wavefunction's absolute value, $|\psi|^2$, gives the probability density function.
3. Wavefunctions must satisfy specific boundary conditions and be normalized to ensure total probability equals one.
4. Solutions to the Schrödinger equation can include both bound states (discrete energy levels) and free states (continuous spectrum).
5. Wavefunctions can exhibit nodes, points where the probability density is zero.

Review Questions

• What does the square of a wavefunction represent in terms of physical interpretation?
• Why must wavefunctions be normalized?
• Explain what is meant by a node in a wavefunction.

Related terms

Schrödinger Equation: A fundamental equation in quantum mechanics that describes how wavefunctions evolve over time.

Probability Density: A measure derived from the square of the absolute value of the wavefunction representing where a particle is likely to be found.

Normalization: The process ensuring that the integral of $|\psi|^2$ over all space equals one, meaning total probability is conserved.