# Did people consider energy quantization of nonlinear oscillators after Planck?

Did people try that? Or did they consider energy quantization for the translation motion of a free particle?

• What is a non-linear oscillator, exactly? Jun 11, 2017 at 9:58
• like with a $x^4$ term in the potential Jun 11, 2017 at 9:59

The Schrodinger equation is linear, so perhaps "quantization of non-linear oscillators" refers to non-linearity of the classical system that one quantizes. If this is what you mean, the answer is yes. In the very first paper on modern quantum mechanics, Heisenberg's paper of 1925, non-linear oscillators with potentials $x^2+cx^3$ and $x^2+cx^4$ play a crucial role. They are called anharmonic oscillators. They were also studied before and after Heisenberg in context of quantization.