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1. Chemical State

   Linked via "time-dependent Schrödinger equation"

   Formal Definition and Quantum Basis
   The chemical state is formally described by the time-dependent wave function, $\Psi(\mathbf{r}, t)$, which is the solution to the time-dependent Schrödinger equation. However, for practical thermodynamic descriptions, the chemical state is often simplified by considering the system to occupy a specific energy eigenstate, $|\psi_n\rangle$, characterized by the [time-…

2. Wavefunction

   Linked via "time-dependent Schrödinger equation"

   Mathematical Formalism and Schrödinger Equation
   The temporal evolution of the wavefunction for a non-relativistic system is governed by the time-dependent Schrödinger equation:
   $$i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r}, t) = \hat{H} \Psi(\mathbf{r}, t)$$

3. Wave Function

   Linked via "time-dependent Schrödinger equation"

   Time Evolution: The Schrödinger Equation
   The temporal dynamics of the wave function are dictated by the time-dependent Schrödinger equation. For a non-relativistic system subject to a time-independent potential $V(\mathbf{r})$, the equation is:
   $$i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r}, t) = \left( -\frac{\hbar^2}{2m} \nabla^2 + V(\mathbf{r}) \right) \Psi(\mathbf{r}, t)$$