Why do we call the psi function the wave' function

[HomogenousCow]

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

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

 

[Vanadium 50]

Because it's a wave equation.

 

[Jano L.]

Why do we call the psi function the "wave' function
When in reality it has little to do with waves.
Sure the Schrödinger equation admits sinusoidal solutions but so does the heat equation.

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 traveling 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.

 

[The_Duck]

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

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 traveling 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.

 

[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.