Wave Function

Rays and Waves  Optics can often be described by rays. Lenses and mirrorsLenses and mirrors DeterministicDeterministic  Light rays follow the path of least time.  Mechanics can be written the same way. Equivalent to minimizingEquivalent to minimizing  Ray optics fails to account for interference.  Theorists in the 1800’s wondered if there should be a wave version of mechanics as well.

Wave Energy  The classical expression for energy is kinetic plus potential. Converted to momentum  A quantized particle in a box has a total energy from its wave. Box length L U = 0 in the box  Waves in the box have nodes on each end. Non-zero ground state energy

Mathematical Model  DeBroglie’s idea gave new direction to this thought. Schrödinger 1925Schrödinger 1925  Schrödinger took the classical energy equation and made it into an abstract wave equation. Differential equationDifferential equation Schrödinger’s wave equationSchrödinger’s wave equation  The wave variable  was called the wavefunction.

Complex Values  Schrödinger’s wave equation requires complex values for the wavefunction . Cannot be directly measuredCannot be directly measured Rough one dimensional form without time dependence  The wavefunction has the properties of a real wave. Superposition Interference and diffraction

Probability Waves  The wavefunction cannot be directly measured and is an information wave. Represents the state of a systemRepresents the state of a system  The square of the wavefunction relates to the probability of a particular measurement occurring. Compare intensity to amplitude of an EM waveCompare intensity to amplitude of an EM wave

Indeterminate Outcome  The wavefunction can be used to predict a probability. Observable variable selected Value established by measurement  The electron in the Bohr atom has a probability of being at a given radius. Radius of Bohr equation most likely next