= Solution
The one-dimensional time-independent <Schrödinger equation> is
$$
\boxed{-\frac{\hbar^2}{2m}\frac{d^2\Psi(x)}{dx^2}+V(x)\Psi(x)=E\Psi(x).}
$$
Here $m$ is the particle <mass>, $V(x)$ its <potential energy>, $E$ the stationary <energy eigenvalue>, and $\hbar=h/(2\pi)$ the reduced <Planck constant>. The spatial <wavefunction> is $\Psi$; the full stationary state is $\Psi(x)e^{-iEt/\hbar}$. Physical bound states satisfy the boundary conditions and <wavefunction normalization> $\int|\Psi|^2dx=1$. The operator on the left is the <Hamiltonian operator>, the sum of kinetic and potential energies.
Back to article page
