schrodinger equation

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Thân thiện
Definition
  1. Noun:
    • The fundamental equation of wave mechanics: The Schrödinger equation is a partial differential equation that describes how the quantum state of a physical system changes over time. It is central to the theory of quantum mechanics, providing a way to calculate the wave function of a system and predict its behavior.
Usage Examples
  • Noun:
    • Solving the Schrödinger equation for a hydrogen atom yields the possible energy levels of its electron.
    • The time-dependent Schrödinger equation is essential for modeling quantum dynamics.
Advanced Usage

  • "Time-independent Schrödinger equation": A specific form of the equation used for systems where the potential energy is not time-dependent, often used to find stationary states and quantized energy levels.

    • The time-independent Schrödinger equation is an eigenvalue problem.

  • "To solve the Schrödinger equation": To find mathematical solutions (wave functions) that satisfy the equation for a given physical setup.

    • Physicists must solve the Schrödinger equation to understand the properties of a quantum well.
Variants and Related Words
  • Wave function (n): The solution to the Schrödinger equation, representing the quantum state of a particle or system.
  • Hamiltonian operator (n): A key operator (denoted by Ĥ) in the Schrödinger equation representing the total energy of the system.
Synonyms
  • Wave equation (in the specific context of quantum mechanics).
Related Phrases
  • "To be governed by the Schrödinger equation": To have behavior that is described by this fundamental law.
    • The behavior of electrons in an atom is governed by the Schrödinger equation.
Noun
  1. the fundamental equation of wave mechanics

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