Schrodinger Wave Equation

The Schrodinger’s Wave Equation is the fundamental equation of physics for describing quantum mechanical behavior. It is also often called the Schrodinger Wave Equation, and is a partial differential equation that describes how the wave function of a physical system evolves over time. Viewing quantum mechanical systems as solutions to the Schrodinger Wave Equation is sometimes known as the Schrodinger Wave picture, as distinguished from the matrix mechanical viewpoint, sometimes known as the Heisenberg picture.

Schrodinger Wave Equation

The time-dependent one-dimensional Schrodinger’s Wave Equation is given by

where i is the imaginary unit, ∑  is the time-dependent wave function, is h-bar, V(x) is the potential, and is the Hamiltonian operator. However, the equation can be separated into temporal and spatial parts using separation of variables ∑ to write

thus obtaining    Schrodinger Wave Equation

Setting each part equal to a constant then gives

(4)
(5)

so

Schrodinger Wave Equation

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