The Schrödinger equation is a fundamental equation in quantum mechanics that describes the behavior of quantum systems. It provides information about the wave function, which represents the state of a quantum system.
The Schrödinger equation itself does not explicitly incorporate the effects of thermal motion or temperature. Instead, it describes the time evolution of the wave function in terms of the system's Hamiltonian operator, which accounts for the system's potential energy and kinetic energy.
However, the effects of thermal motion and temperature can be taken into account by considering the statistical mechanics of the quantum system. In statistical mechanics, the behavior of a system composed of many particles, including quantum particles, can be described using probability distributions. The most common framework for statistical mechanics is the density matrix formalism.
The density matrix allows for the description of mixed states, which can account for thermal effects. A mixed state represents a statistical ensemble of quantum states, each with a certain probability. The density matrix formalism provides a way to calculate statistical averages, including those related to temperature and thermal fluctuations.
In summary, while the Schrödinger equation itself does not directly incorporate thermal motion, the effects of temperature and thermal fluctuations can be accounted for by considering the statistical mechanics of the quantum system using the density matrix formalism.