# Why do we call the psi function the wave' function

1. Jul 12, 2013

### HomogenousCow

Why do we call the psi function the "wave' function

When in reality it has little to do with waves.
Sure the schrodinger equation admits sinusoidal solutions but so does the heat equation.

2. Jul 12, 2013

Staff Emeritus
Because it's a wave equation.

3. Jul 13, 2013

### Jano L.

You are right, the function $\psi$ has little to do with waves and ordinary wave equation. The reason is partly historical and partly the difficulty with proper interpretation of the function $\psi$. de Broglie's idea that particles travelling in one direction are guided by some kind of wave motivated Schroedinger to invent his equation for this wave. The meaning of the function $\psi$ in the equation was unclear even to Schroedinger, but the name wave function seemed apropriate since the de Broglie wave is a solution of the simplest Schroedinger equation. Then it was found out that the equation has also many other solutions that are not waves, but the name sticked.

It is said that Einstein did not use the name "wave function" but instead used "$\psi$-function", perhaps for the same reason you are asking.

4. Jul 13, 2013

### The_Duck

Because the equation has solutions that take the form of traveling waves, $\psi(x, t) = e^{i k x - i \omega t}$. This is a travelling sinusoidal wave.

The heat equation does not have solutions that look like traveling waves: its sinusoidal solutions look like $\phi(x, t) = e^{i k x - \omega t}$. Note the crucial difference in the time dependence.

Last edited: Jul 13, 2013
5. Jul 13, 2013

### lavinia

Mathematically, the Shroedinger equation is like the heat equation except that it can take on complex values.
States follow a continuous Markov like process with amplitudes replacing probabilities. See Feynmann's Lectures on Physics Vol3 for a derivation from a discrete process of amplitude transitions.

One reason the Shroedinger equation may be thought of as wave equation might be because wave functions interfere linearlly, like linear waves.