= Solution
The one-dimensional <time-independent Schrödinger equation> is
$$
\boxed{-\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2}+V(x)\psi(x)=E\psi(x).}
$$
The differential term is the <kinetic energy> operator acting on the <wave function>, $V(x)$ supplies the multiplicative <potential energy>, and their sum is the <Hamiltonian operator>. The eigenvalue $E$ is the stationary state's total <energy>. This form assumes a nonrelativistic particle, a time-independent scalar potential, and no additional internal degrees of freedom in the stated model.
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