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Wavefunction

A mathematical function that describes the quantum state of a system, containing information about the probability distribution of the particle's properties.
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The statement of the theorem

Let H^\hat{H} be the Hamiltonian operator for a system of NN particles, and let Ψ(r1,…,rN)\Psi(\mathbf{r}_1, \dots, \mathbf{r}_N) be the wavefunction. The wavefunction must satisfy the time-independent Schrödinger equation:\nH^Ψ=EΨ\hat{H}\Psi = E\Psi\nwhere H^=∑i=1N(−ℏ22mi∇i2+V(ri))\hat{H} = \sum_{i=1}^{N} \left(-\frac{\hbar^2}{2m_i}\nabla_i^2 + V(\mathbf{r}_i)\right) is the Hamiltonian, and EE is the total energy eigenvalue.