# Why doesn't an electron lose energy when tunneling?

Through my classwork I have learned that an electron will not lose energy when it is tunneling. However, I am having a hard time understanding why.

From what I understand, as soon as the electron hits the barrier its wave function will be $\Psi(x)=Ae^{-\alpha x}$ where $\alpha = \sqrt{\frac{2m(U_0 -E)}{\hbar}}$. As the electron tunnels, I know its amplitude decreases and $x$ will increase as the particle moves past the barrier. Is this somehow related to the electron not losing energy? Or is there a different reason why?

There's the amplitude of the wave function $|\psi(x)|^2$ which tells you how likely it is to find the particle at the position $x$ and there is the energy of $E$ the particle, these two have nothing to do with each other. Since your looking at at solutions of the stationary Schrödinger equation this has to be constant.