请用英文润色以下段落： Assume $\hbar$ and $m$ be 1

Assuming $\hbar$ and $m$ are both equal to 1, we can simplify the Schrödinger equation to the form of $-\frac{1}{2} \frac{\partial^2 \psi}{\partial x^2} + V(x)\psi = E\psi$. This equation is used to describe the behavior of particles in a potential field. By solving this equation, we can obtain the wave function $\psi$ which represents the probability density of finding the particle at a specific position. The energy eigenvalues obtained from this equation represent the energy levels of the particle. Therefore, the Schrödinger equation is a fundamental equation in quantum mechanics that provides insight into the behavior of particles in a potential field.