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.
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 
Setting each part equal to a constant then gives
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(4) |
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(5) |
so
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