Schrodinger wave equation
Noun: - The fundamental equation of wave mechanics: A partial differential equation that describes how the quantum state of a physical system changes over time. It is central to non-relativistic quantum mechanics, determining the wave function of a system.
This term is used exclusively in the context of theoretical and quantum physics. It names a specific, foundational mathematical formula. - The Schrodinger wave equation is used to predict the behavior of electrons in an atom. - Solving the Schrodinger wave equation for a given potential yields possible energy states.
- Time-dependent Schrodinger equation: The general form that includes time evolution of the wave function.
- Time-independent Schrodinger equation: A specific form used for stationary states, where the potential is not time-dependent. This is often what is meant in basic quantum mechanics courses.
- For a system in a stationary state, we use the time-independent Schrodinger wave equation.
- Schrodinger equation: A common, shortened form of the full term "Schrodinger wave equation." The terms are often used interchangeably.
- Wave function: The solution to the Schrodinger wave equation, representing the quantum state.
- Hamiltonian operator: A key component (Ĥ) within the Schrodinger equation representing the total energy of the system.
- Schrodinger equation (the most direct synonym)
- Wave equation (in the specific context of quantum mechanics, though this can be ambiguous with classical wave equations)
This term refers strictly to the specific equation formulated by Erwin Schrödinger. It does not refer to a general concept of "waves" or "equations" outside this precise scientific context. The equation itself is not a "thing" that waves, but a mathematical rule governing the wave function's behavior.
- the fundamental equation of wave mechanics