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A double oscillator is characterized by potential $V\left(x\right)=\frac{m{\omega }^2}{2}{\left(\left|x\right|-x_0\right)}^2$. With $x_0=0$ the potential of the harmonic oscillator is obtained. It is not possible to analytically solve the Schrödinger equation. We set the parameters: $\hslash =1$; $m=1$; $\omega =1$.
Eigenvalues: single oscillator $\left(x_0=0\right)$ vs double oscillator $\left(x_0=1\right)$.
Eigenvalues and Eigenfunctions: single oscillator $\left(x_0=0\right)$ vs double oscillator $\left(x_0=1\right)$.