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→Mathematical forms: + ls's
from which Schrödinger's equation and the eigenvalue problem <math> \hat H\Psi = E\Psi</math> can be easily seen.
from which Schrödinger's equation and the eigenvalue problem <math> \hat H\Psi = E\Psi</math> can be easily seen.
===Time-independent Schrödinger Equation===
===Time-independent Schrödinger Equation===
<math>\psi(x)</math> is often called the "wavefunction", though strictly speaking it is <math>\Psi(x,t)</math> that is the wavefunction.
<math>\psi(x)</math> is often called the "wavefunction", though strictly speaking it is <math>\Psi(x,t)</math> that is the wavefunction.
===Solutions to the Schrödinger Equation===
===Solutions to the Schrödinger Equation===
Since the Schrödinger equation is [[Linear equations|linear]], if <math>\psi_1 (x)</math> and <math>\psi_2 (x)</math> are solutions, then <math>\psi_1 (x) + \psi_2 (x)</math> is also a solution.
Since the Schrödinger equation is [[Linear equations|linear]], if <math>\psi_1 (x)</math> and <math>\psi_2 (x)</math> are solutions, then <math>\psi_1 (x) + \psi_2 (x)</math> is also a solution.
===Eigenvalue problems===
===Eigenvalue problems===
One example of this type of eigenvalue problem is an electrons bound inside an [[atom]].
One example of this type of eigenvalue problem is an electrons bound inside an [[atom]].
===Interpretation of the Wavefunction===
===Interpretation of the Wavefunction===